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prove that sin theta +cos theta /sin theta - cos theta +sin theta - cos theta /sin theta +cos theta
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trigonometry class 10.
sin theta+cos theta/sin theta-cos theta+sin theta-cos theta/sin theta+cos theta=2 sec square theta/tan square theta-1. Prove that sina+cosa/sina-cosa+sina-cosa/sina+cosa=2sec2a/tan2a-1.
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Here we have started the series for trigonometry extra questions. And you are going to get a complete set of extra questions that you must study. This series of questions for trigonometry class 10 will help you to understand the conceptual study of trigonometry. The other questions that you must study for trigonometry class 10 are as follows:
Q-1:
Prove the following trigonometric identities | R S Aggarwal example 1 |
Q-2:
Prove that (tan theta + sin theta)/(tan theta - sin theta) = (sec theta +1)/(sec theta -1).
Q-3:
Prove that 1/(1+sin theta)+1/(1-sin theta)=2 sec^(2)theta
Q-4:
Exercise 8.4 class 10 question 5 part 2.
Q-5:
Prove that cos theta/(1+sin theta)=(1-sin theta)/cos theta. Prove that (1-cos theta)/sin theta=sin theta/(1+cos theta).
Q-6:
Prove that sin theta/(1-cos theta)=(cosec theta+cot theta)
Q-7:
Prove that (1-sin theta)/(1+sin theta)=(sec theta-tan theta)^2
Q-8:
Prove that root(1+sin theta/1- sin theta)+root(1-sin theta/1+sin theta)=2 sec theta.
Q-9:
Prove that root (1+sin theta/1-sin theta)=sec theta+tan theta. Exercise 8.4 question 5(vi).
Q-10:
Prove that cosec theta/(cosec theta-1) + cosec theta/(cosec theta+1)=2sec^2 theta.
Q-11:
Prove that cos theta/1-tan theta + sin theta/1-cot theta=sin theta+cos theta.
Q-12:
prove that tan theta/1-cot theta+cot theta/1-tan theta=1+sec theta cosec theta. Ex 8.4 Question 5 (iii):
Q-13:
Prove that (1+cota-coseca)(1+tana+seca)=2. Prove that (1+cotθ-cosecθ)(1+tanθ+secθ)=2
Q -14:
RD Sharma Example-7 | Prove that sin theta/(1-cos theta)+tan theta/(1+cos theta)=sec theta cosec theta+cot theta
Q -15:
RD Sharma Exercise 11.1 class 10 Example-11. Prove that cosa/1-tana+sin2a/sina-cosa=sina+cosa.
Q-16(a):
If sec theta + tan theta=p, show that p^2-1/p^2+1=sin theta
Q-16(b):
If 3 sin theta + 5 cos theta=5, prove that 5 sin theta-3 cos theta=+-3
Q-17:
If acosθ bsinθ=c prove that asinθ+bcosθ= ±√a2+b2-c2
Q-18:
If sec theta=x+1/4x, show that sec theta+tan theta=2x or 1/2x
Q-19:
prove that 1/(cosec theta - cot theta)-1/sin theta=1/sin theta-1/(cosec theta + cot theta)
Q-20:
If cos theta+sin theta=√2 cos theta, then show that cosθ-sinθ = √ 2sinθ
Q-21:
If tan theta=p/q, show that (p sin theta-q cos theta)/(p sin theta+q cos theta)=(p^2-q^2)/(p^2+q^2)
Q-22:
Prove that sin theta / cot theta+cosec theta=2+sin theta/cot theta-cosec theta
Q-23:
If sin theta + sin^2 theta = 1, show that cos^2 theta + cos^4 theta = 1
Q-24:
Prove that sin^6x+cos^6x=1-3 sin^2x cos^2x
Q-25:
prove that sec theta + tan theta -1/tan theta-sec theta+1= cos theta/1-sin theta
Q-26:
If 7sin^2 theta+3cos^2 theta=4 show that tan theta= 1/√3
Q-27:
If x sin^3 theta + y cos^3 theta = sin theta cos theta , prove that x^2+y^2=1
Q-28:
Prove that sin theta +cos theta /sin theta - cos theta +sin theta - cos theta /sin theta +cos theta=2 sec square theta /tan square theta -1
Q-29:
Prove that tan2A-tan2B=sin2A-sin2B/cos2Acos2B=cos2B-cos2A/cos2Acos2B
Q-30:
If a+b=90 then prove that root tanAtanB+tanAcotB/sinAsecB-sin2B/cos2A=tanA
Q-31:
If tana=ntanb and sina=msinb prove that cos^2a=m^2-1/n^2-1
Q-32:
Prove that (1+sina-cosa/1+sina+cosa)^2=1-cosa/1+cosa
Q-33:
If cosec theta - sin theta = l and sec theta - cos theta = m, then prove that l^2m^2(l^2+m^2+3)=1
Q-34:
If √3 cot^2θ - 4cotθ+ √3 =0, then find the value of cot^2θ + tan^2θ
Q-35:
If tan theta+sin theta=m and tan theta-sin theta=n then prove that m^(2)-n^(2)=4sqrt(mn)
Q-36:
If 1+sin^2 theta=3 sin theta cos theta, then prove that tan theta=1 or 1/2.
Q-37:
If tan theta+sec theta=l, then prove that sec theta=(l^2)+(1/2l)
sin theta+cos theta/sin theta-cos theta+sin theta-cos theta/sin theta+cos theta=2 sec square theta/tan square theta-1. Prove that sina+cosa/sina-cosa+sina-cosa/sina+cosa=2sec2a/tan2a-1.
#trigonometrybyavisir #trigonometryclass10avijainclasses #trigonometryavijainclasses #trigonometry #trigonometryclass10 #trigonometrybyavisir
Here we have started the series for trigonometry extra questions. And you are going to get a complete set of extra questions that you must study. This series of questions for trigonometry class 10 will help you to understand the conceptual study of trigonometry. The other questions that you must study for trigonometry class 10 are as follows:
Q-1:
Prove the following trigonometric identities | R S Aggarwal example 1 |
Q-2:
Prove that (tan theta + sin theta)/(tan theta - sin theta) = (sec theta +1)/(sec theta -1).
Q-3:
Prove that 1/(1+sin theta)+1/(1-sin theta)=2 sec^(2)theta
Q-4:
Exercise 8.4 class 10 question 5 part 2.
Q-5:
Prove that cos theta/(1+sin theta)=(1-sin theta)/cos theta. Prove that (1-cos theta)/sin theta=sin theta/(1+cos theta).
Q-6:
Prove that sin theta/(1-cos theta)=(cosec theta+cot theta)
Q-7:
Prove that (1-sin theta)/(1+sin theta)=(sec theta-tan theta)^2
Q-8:
Prove that root(1+sin theta/1- sin theta)+root(1-sin theta/1+sin theta)=2 sec theta.
Q-9:
Prove that root (1+sin theta/1-sin theta)=sec theta+tan theta. Exercise 8.4 question 5(vi).
Q-10:
Prove that cosec theta/(cosec theta-1) + cosec theta/(cosec theta+1)=2sec^2 theta.
Q-11:
Prove that cos theta/1-tan theta + sin theta/1-cot theta=sin theta+cos theta.
Q-12:
prove that tan theta/1-cot theta+cot theta/1-tan theta=1+sec theta cosec theta. Ex 8.4 Question 5 (iii):
Q-13:
Prove that (1+cota-coseca)(1+tana+seca)=2. Prove that (1+cotθ-cosecθ)(1+tanθ+secθ)=2
Q -14:
RD Sharma Example-7 | Prove that sin theta/(1-cos theta)+tan theta/(1+cos theta)=sec theta cosec theta+cot theta
Q -15:
RD Sharma Exercise 11.1 class 10 Example-11. Prove that cosa/1-tana+sin2a/sina-cosa=sina+cosa.
Q-16(a):
If sec theta + tan theta=p, show that p^2-1/p^2+1=sin theta
Q-16(b):
If 3 sin theta + 5 cos theta=5, prove that 5 sin theta-3 cos theta=+-3
Q-17:
If acosθ bsinθ=c prove that asinθ+bcosθ= ±√a2+b2-c2
Q-18:
If sec theta=x+1/4x, show that sec theta+tan theta=2x or 1/2x
Q-19:
prove that 1/(cosec theta - cot theta)-1/sin theta=1/sin theta-1/(cosec theta + cot theta)
Q-20:
If cos theta+sin theta=√2 cos theta, then show that cosθ-sinθ = √ 2sinθ
Q-21:
If tan theta=p/q, show that (p sin theta-q cos theta)/(p sin theta+q cos theta)=(p^2-q^2)/(p^2+q^2)
Q-22:
Prove that sin theta / cot theta+cosec theta=2+sin theta/cot theta-cosec theta
Q-23:
If sin theta + sin^2 theta = 1, show that cos^2 theta + cos^4 theta = 1
Q-24:
Prove that sin^6x+cos^6x=1-3 sin^2x cos^2x
Q-25:
prove that sec theta + tan theta -1/tan theta-sec theta+1= cos theta/1-sin theta
Q-26:
If 7sin^2 theta+3cos^2 theta=4 show that tan theta= 1/√3
Q-27:
If x sin^3 theta + y cos^3 theta = sin theta cos theta , prove that x^2+y^2=1
Q-28:
Prove that sin theta +cos theta /sin theta - cos theta +sin theta - cos theta /sin theta +cos theta=2 sec square theta /tan square theta -1
Q-29:
Prove that tan2A-tan2B=sin2A-sin2B/cos2Acos2B=cos2B-cos2A/cos2Acos2B
Q-30:
If a+b=90 then prove that root tanAtanB+tanAcotB/sinAsecB-sin2B/cos2A=tanA
Q-31:
If tana=ntanb and sina=msinb prove that cos^2a=m^2-1/n^2-1
Q-32:
Prove that (1+sina-cosa/1+sina+cosa)^2=1-cosa/1+cosa
Q-33:
If cosec theta - sin theta = l and sec theta - cos theta = m, then prove that l^2m^2(l^2+m^2+3)=1
Q-34:
If √3 cot^2θ - 4cotθ+ √3 =0, then find the value of cot^2θ + tan^2θ
Q-35:
If tan theta+sin theta=m and tan theta-sin theta=n then prove that m^(2)-n^(2)=4sqrt(mn)
Q-36:
If 1+sin^2 theta=3 sin theta cos theta, then prove that tan theta=1 or 1/2.
Q-37:
If tan theta+sec theta=l, then prove that sec theta=(l^2)+(1/2l)
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