Question

What is the value of :-
$\sin^{2}a+ 1 \div 1 + \tan^{2}a$

Answer 1

we know that
${ \sec }^{2} a = 1 + { \tan }^{2} a$
so by this 1+sin^2(a) / 1+tan^2(a)
= 1+sin^2(a) /sec^2(a) = cos^2(a)[1+sin^2(a)]
= 1-sin^2(a) * 1+sin^2(a)
this is in the form of (a-b) (a-b) = a^2-b^2
so = 1-sin^4(a)
hence the answer is 1-sin^4(a)