Prove:sin2 A cot2 A + cos2 A tan2 A = 1

1.	Prove:sin2 A cot2 A + cos2 A tan2 A = 1
Answer» We know that, cot² A = \(\frac{cos^2 A}{sin^2 A}\) and tan² A = \(\frac{sin^2 A}{cos^2 A}\) Substituting the above in L.H.S, we get L.H.S = sin² A cot² A + cos² A tan² A = {sin² A (\(\frac{cos^2 A}{sin^2 A}\))} + {cos² A (\(\frac{sin^2 A}{cos^2 A}\))} = cos² A + sin² A = 1 [∵ sin² θ + cos² θ = 1] = R.H.S Hence Proved

Answer»

We know that,

cot² A = \(\frac{cos^2 A}{sin^2 A}\) and tan² A = \(\frac{sin^2 A}{cos^2 A}\)

Substituting the above in L.H.S, we get

L.H.S = sin² A cot² A + cos² A tan² A

= {sin² A (\(\frac{cos^2 A}{sin^2 A}\))} + {cos² A (\(\frac{sin^2 A}{cos^2 A}\))}

= cos² A + sin² A = 1 [∵ sin² θ + cos² θ = 1]

= R.H.S

Hence Proved

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