Trigonometry Part 7 | Top Questions On Basic Identity By Abhinay Sharma (Abhinay Maths)

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

The main functions in trigonometry are Sine, Cosine and Tangent. They are simply one side of a right-angled triangle divided by another. For any angle "θ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)

Trigonometry is defined as one of the branches of mathematics that deals with the relationships that involve lengths and also the angles of triangles. In a simple manner, we can say that Trigonometry is the study of triangles.

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[ABHINAYMATHS]

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[krissh]

आदरणीय सर हर किसी के पास दिल्ली आकर पढ़ने का सपना होता है मन में यह भावना भी होती है कि वहां पर सुविधाओं और गुणवत्तापूर्ण संसाधनों का लाभ उठा सकें दूरस्थ छात्र इस सराहनीय निस्वार्थ प्रयास प्रयास से लाभान्वित होते हैं आप जैसे अध्यापक ही कलाम साहब के सपने साकार करने के सबसे बड़े माध्यम है

[Mrnish]

Solutions-
6) 2sinx +15cos^2x=7
2sinx+15(1-sin^2x)=7
15sin^2x-2sinx-8=0
Solve to get sinx=4/5
Cosx=3/5(by triplet)
So cotx=3/4(ans)

7) 2-cos^x=3sinxcosx
Divide both sides by cos^2x
2/cos^2x - 1= 3.sinx/cosx
2sec^2x-1= 3tanx
2(tan^2x+1)-1=3tanx
2tan^2x-3tanx+1=0
Solve the quad eqn
Tanx=1 or 1/2(ans)

8)1+
It's a GP of infinte terms
1st term(a)=1
Common ratio(r)=sinx
a/1-r=4+2√3
1/1-sinx=4+2√3
1-sinx=1/4+2√3
Rationalize to get sinx=√3/2
So x=pie/3(ans)


Make lhs in sin form
Use identity cos^2x=1-sin^2x
Solve to get (sin^2x-sin^2y)^2=0
Or sin^2x=sin^2y
So x=y
And therefore cos^2x=cos^2y
Put in eqn cos^4y/cos^2x+sin^4y/sin^2x
Ans will be 1.
#AbhinavMaths sir if I am wrong do correct me 🙏🙏

[malaypangtey]

6th cotx =15/2
7th
 2 - (cos x)^2 = 3*sin x * cos x
Divide both sides by (cos x)^2
2 /(cos x)^2 - 1 = 3 * sinx/ cos x
2 (Sec x)^2 - 1 = 3 tan x

If tan x = t then (Sec x)^2 = 1+t^2
Therefore we have
2 + 2*t^2 - 1 = 3t
2t^2 - 3t + 1 = 0
2t^2 - 2t - t + 1 = 0
(2t-1)(t-1) = 0
So t = 1 or 1/2

[amit]

किस कदर शुक्रिया अदा करूं मैं आपका,
आपका धन्यवाद करने मुझे अल्फ़ाज़ नहीं मिलते,
TRIGONOMETRY वाकई इतनी खूबसूरत न होती,
अगर हमें आपके जैसे गुरु न मिलते ।

अभिनय सर आपका बहुत बहुत धन्यवाद ।

[beinghneha]

Ek request hai sir. Aap plz agr jo homework dete hain use next video me smjha diya way me ji shi but plz sir, humble request hai aapse??

[prashantdave]

Sir 1st question m ans. -2 h
Sorry sir par Mera dhyan Gaya to mene bolo Diya.
And video to aapki best hi rehti h

[Er.SurendraKumar]

Solution of Question No. 6
2sinα +15cos²α =7
We know that cos²α = 1-sin²α
2sinα +15cos²α =7
put 1-sin²α instead of cos²a
2sinα +15(1-sin²α) =7
-15sin²α +2sinα +8=0 => (form of a quadratic equation)
-15 sin²α +12 sinα - 10 sinα +8=0
(after solving)
sinα = 4/5 or -2/3 (which is not possible, because sinα lies only -1 to 1)
From triplet 3, 4, 5
Cotα = 3/4

[pattavarayanc]

Sir at least please provide 2 classes everyday... Pls sir...We all are expecting that from U. This is my humble request..Pls sir ji...

[ravimaurya]

hey guys... i think in Q6 this should be 15Cos^2@ in order to obtain 3/4 as answer....otherwise it will give a faulty answer 15/2.

[RahulKumar-ptpi]

Sir compound interest aur installment pe bhi ek class

[akanshagupta]

Sir.. pls help in solving below question:

If A be a positive acute angle satisfying cos²A + cos⁴A=1, then the value of tan²A + tan²B is:

a. 3/2
b. 1
c. 1/2
d. 0

[yogeshola]

Such a nice person .I never seen such type of personality.a great human being .I like two people very much.one shri atal Bihari Bajpai and second mr.abhinay.

[ashishkumar.]

sin²a +cos²a =1 (identity)

cos²a = 1-sin²a

2sina +15cos²a =7

put 1-sin²a instead of cos²a

2sina +15(1-sin²a) =7

-15sin²a +2sina +8=0 => (form of a quadratic equation)

sina =t

-15t² +2t +8=0

t= 4/5 and t = -2/3 => (after using quadratic formula)

t = 4/5 is the real solution (the other one makes a negative angle)

sina= 4/5

sin²a = 16/25 => (after squaring both sides)

remember identity sin²a+cos²a=1 => sin²a = 1-cos²a

1-cos²a =16/25 => cos²a =9/25 => cosa =3/5 ( the other solution -3/5 makes negative angle)

cota = cosa / sina = > (3/5) / (4/5) = 3/4

[prataykshmishra]

❣️❣️❣️❣️❣️❣️❣️❣️ अभिनय सर, बेमिसाल हैं आप !!

[ArjunSingh-lsbq]

Very down to earth...no attitude....love u from Lucknow

[GopalKumar-hkjg]

Aap bahut achchha read karate hai. Aap to trigonometry ka Hero hai. So i like you sir. Thank you sir

[roy_ranjeet]

The most innovative part of ur videos is the theme songs which are played in the beginning... awesome collection sir ji...

[fairojashaik]

sir please explain the question that u gave as homework.

[rishavmanav]

sir its an humble request if u can provide the solution of the que. provided as homework. it would be highly helpfull .. please sir