Trigonometric functions - II | NIOS Class 12 Maths Chapter 4 | Terminal exercise Solution

Trigonometric function - II , Chapter 4, NIOS Class 12, Maths 311 Terminal exercise solution

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Addition and Multiplication of Trigonometric Functions, Transforrmation of products into sums and vice versa, Trigonometric functions of multiples and submultiples of angles, Trigonometric Equations,

solved, prove, proofs

1. Prove that tan(A + B) tan(A - B) = (cos^2 B - cos^2 A)/(cos^2 B - sin^2 A)
2. Prove that cos theta - sqrt 3 sin theta = 2 cos(theta + Pi/3)
3a. If A + B = Pi/4 then prove that (1 + tan A )(1 + tan B) = 2
3b. If A + B = Pi/4 then prove that (cot A - 1 )(cot B - 1) = 2
4a. prove sin(A - B )/(cosA cosB) + sin(B - C)/(cosB cosC) + sin(C - A)/(cosC cosA) = 0
b. prove cos(Pi/10 - A) cos(Pi/10 + A) + cos (2Pi/5 - A) cos(2Pi/5 - A) = cos 2A
c. prove cos 2Pi/9 cos 4Pi/9 cos 8Pi/9 = -1/8
d. prove cos 13Pi/45 + cos 17Pi/45 + cos 43Pi/45 = 0
e. prove tan(A + Pi/6) + cot(A - Pi/6) = 1/(sin 2A - sin Pi/3)
f. prove (sin theta + sin 2 theta)/(1 + cos theta + cos 2 theta) = tan theta
g. prove (cos theta + sin theta )(cos theta - sin theta ) = tan 2 theta + sec 2 theta
h. prove (1 - sin theta)(1 + sin theta ) = tan^2 (Pi/4 - theta/2)
i. prove cos2 A + cos2 (A + Pi/3) + cos2 (A - Pi/ 3) = 3/2
j. prove (sec 8A - 1 )/(sec 4A - 1)= tan 8A/tan 2A
k. prove cos Pi/30 cos 7Pi/30 cos 11Pi/30 cos 13Pi/30 = 1/16
l. prove sin Pi/10 + sin 13Pi/10 = - 1/2
5. Find the general value of 'theta' satisfying
(a) sin theta = 1/2
(b) sin theta = sqrt3/2
(c) sin theta = -1/sqrt 2
(d) cosec theta = sqrt 2
6. Find the general value of 'theta' satisfying
(a) cos theta = 1/2
(b) sec theta = 2/sqrt 3
(c) cos theta = -sqrt 3/2
(d) sec theta = -2
7. Find the general value of 'theta' satisfying
(a) tan theta = 1
(b) tan theta = -1
(c) cot theta = -1/sqrt 3
8. Find the general value of 'theta' satisfying
(a) sin^2 theta = 1/2
(b) 4 cos^2 theta = 1
(c) 2cot^2 theta = cosec^2 theta

9. Solve the following for theta :
(a) cos p theta = cos q theta
(b) sin 9 theta = sin theta
(c) tan 5 theta = cot theta

10 Solve for theta
a. sin m theta + sin n theta = 0
b. tan m theta + cot n theta = 0
c. cos theta + cos 2 theta + cos 3 theta = 0
d. sin theta + sin 2 theta + sin 3 theta + sin 4 theta = 0

00:00 0. Exercise in this Video
00:04 1. Prove that tan(A + B)tan(A - B) = (cos^2 B - cos^2 A)/(cos^2 B - sin^2 A)
01:53 2. Prove that cosθ - √3sinθ = 2cos(θ + π/3)
02:34 3a. If A + B = π/4 then prove that (1 + tan A )(1 + tan B) = 2
03:47 3b. If A + B = π/4 then prove that (cot A - 1 )(cot B - 1) = 2
05:05 4a. Prove sin(A - B )/(cosA cosB) + sin(B - C)/(cosB cosC) + sin(C - A)/(cosC cosA) = 0
05:54 4b. Prove cos(π/10 - A) cos(π/10 + A) cos (2π/5 - A) cos(2π/5 - A) = cos 2A
07:20 4c. Prove cos 2π/9 cos 4π/9 cos 8π/9 = -1/8
09:14 4d. Prove cos 13π/45 + cos 17π/45 + cos 43π/45 = 0
10:18 4e. Prove tan(A + π/6) + cot(A - π/6) = 1/(sin 2A - sin π/3)
11:24 4f. Prove (sinθ + sin 2θ)/(1 + cosθ + cos 2θ) = tanθ
12:04 4g. Prove (cosθ + sinθ )(cosθ - sinθ ) = tan 2θ + sec 2θ
12:58 4h. Prove (1 - sinθ)(1 + sinθ ) = tan^2 (π/4 - θ/2)
14:03 4i. Prove cos2 A + cos2 (A + π/3) + cos2 (A - π/ 3) = 3/2
14:59 4j. Prove (sec 8A - 1 )/(sec 4A - 1)= tan 8A/tan 2A
16:20 4k. Prove cos π/30 cos 7π/30 cos 11π/30 cos 13π/30 = 1/16
17:39 4l. Prove sin π/10 + sin 13π/10 = - 1/2
18:23 5. Find the general value of 'θ ' satisfying (a) sinθ = 1/2 (b) sinθ = √3/2 (c) sinθ = -1/√2 (d) cosecθ = √2
19:38 6. Find the general value of 'θ ' satisfying (a) cosθ = 1/2 (b) secθ = 2/√3 (c) cosθ = -√3/2 (d) secθ = -2
20:54 7. Find the general value of 'θ ' satisfying (a) tanθ = 1 (b) tanθ = -1 (c) cotθ = -1/√3
21:59 8. Find the general value of 'θ ' satisfying (a) sin^2 θ = 1/2 (b) 4 cos^2 θ = 1 (c) 2cot^2 θ = cosec^2 θ
23:52 9. Solve the following forθ : (a) cos pθ = cos qθ (b) sin 9θ = sinθ (c) tan 5θ = cotθ
25:47 10a. Solve for θ : sin mθ + sin nθ = 0
26:41 10b. Solve for θ : tan mθ + cot nθ = 0
27:39 10c. Solve for θ : cosθ + cos 2θ + cos 3θ = 0
28:45 10d. Solve for θ : sinθ + sin 2θ + sin 3θ + sin 4θ = 0
30:32 End