Question

Sin^2Acot^a+cos^2Atan^2a=1

Answer 1

●heya it's Aastha...

◆taking LHS.

Sin^2Acot^a+cos^2Atan^2a

Sin^2A × cos^2A/ sin^2 A + cos^2 × sin^2 / cos^2. { cot = sin/ cos . tan = sin/cos }

Cos^2 + Sin^2 { Sin^2 + cos ^2 = 1 }

1 .

LHS= RHS.

hence proved...

Answer 2

To prove:$sin^2Acot^2A+cos^2Atan^2A=1$
Consider LHS:
$=(sin^2A)\frac{(cos^2A)}{(sin^2A)}+(cos^2A) \frac{(sin^2A)}{(cos^2A)}$
$=sin^2A+cos^2A$
By using identity,
=1
=RHS
LHS = RHS
Hence, proved.