Question

Prove the following trigonometric identities. $(1+cot^{2}A)sin^{2}A=1$

Answer 1

Answer with Step-by-step explanation:

Given : (1 + Cot² A) Sin² A = 1

L.H.S :   (1 + Cot² A) Sin² A  

= Cosec² A Sin² A

[By using the identity ,cot² θ + 1 = cosec² θ]

= (Cosec A Sin A)²

= (1/Sin A x Sin A )²

[By using the identity ,Cosec A = 1/Sin A]

= (1)²

= 1

(1 + Cot² A) Sin² A = 1

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer

$\tt{(cot^{2} + 1)sin^{2} A}$

=> cosec^2 A sin^2 A [cot^2 Ø + 1 = cosec^2 Ø]

=> 1

Hence Proved.