Question

2+tan^2(A)+cot^2(A) = 1/sin^2(A)-sin^4(A)

Answer 1

hope this helps you mate

Answer 2

Answer:

$\green{\huge{True}}$

Step-by-step explanation:

$2+\tan ^2\left(a\right)+\cot ^2\left(a\right)=\frac{1}{\sin ^2\left(a\right)-\sin ^4\left(a\right)}}$

$=\frac{\cos ^4\left(a\right)+\sin ^4\left(a\right)+2\cos ^2\left(a\right)\sin ^2\left(a\right)}{\cos ^2\left(a\right)\sin ^2\left(a\right)}$

$=\frac{\left(\cos ^2\left(a\right)+\sin ^2\left(a\right)\right)^2}{\cos ^2\left(a\right)\sin ^2\left(a\right)}$

$=\frac{\left(\cos ^2\left(a\right)+\sin ^2\left(a\right)\right)^2}{\cos ^2\left(a\right)\sin ^2\left(a\right)}$

$=\frac{1}{\sin ^2\left(a\right)\cos ^2\left(a\right)}$

$=\frac{1}{\left(1-\sin ^2\left(a\right)\right)\sin ^2\left(a\right)}$

$\Rightarrow \mathrm{True}$

Hence Proved.

$\orange{\huge{\boxed{\mathfrak{Hope \:its\:help\:You}}}}$