Question

Prove the following trigonometric identities. $sin^{2}A+\frac{1}{1+tan^{2}A}=1$

Answer 1

Answer with Step-by-step explanation:

Given : sin²A +1/(1+ tan²A) = 1

L H.S : sin²A + 1/(1+ tan²A)

= sin²A + 1/sec²A

[By using the identity ,1 + tan²θ = sec²θ]

= sin²A +(1/secA)²

= sin²A + cos²A

[By using the identity ,1 /secθ = cosθ]

= 1

[By using the identity , sin² θ + cos² θ = 1]

sin²A +1/(1+ tan²A) = 1

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer:

Yes

Step-by-step explanation:

(sinA)^2 + secA)^2

= (sinA)^2 + (cosA)^2 = 1