Question

(1+ tan^2 A)+(1+1/tan^2A)
=1/sin2A - sin4 A​

Answer 1

Step-by-step explanation:

{1/tan = cot, $1+ tan^2 = sec^2$, $1+cot^2 = cosec^2$}

(1+ $tan^{2}$A)+(1+$cot^{2}$A)

$sec^{2} + cosec^2$

$\frac{1}{cos^2} + \frac{1}{sin^2}$ = $\frac{sin^2 +cos^2}{sin^2cos^2}$

$\frac{1}{sin^2 cos^2}$ ($cos^2$ = 1 -$sin^{2}$)

$\frac{1}{sin^2 (1 - sin^2)}$ = $\frac{1}{sin^2 - sin^4}$

hence proved