Question

prove cos^2theta(1+tan^2theta)=1​

Answer 1

$Given \: \: Question \: \: Is \: \: \\ \\ \cos {}^{2} (x) \times (1 + \tan {}^{2} (x)) = 1 \\ \\ LH S \: \: \: \: \: \: \: \: \\ \\ \cos {}^{2} (x) \times (1 + \tan {}^{2} (x) ) \\ \\ \cos {}^{2} (x) \times \sec {}^{2} (x) \\ \\ \cos {}^{2} (x) \times \frac{1}{ \cos {}^{2} (x) } \\ \\ = 1 \: \: hence \: \: proved \\ \\ Note \: \: \\ \\ 1) \: \: \: 1 + \tan {}^{2} (x) = \sec {}^{2} (x) \\ \\ 2) \: \: \: \sec {}^{2} (x) = \frac{1}{ \cos {}^{2} (x) }$

Answer 2

Cos^2 theta (1+tan^2theta)=1

LHS

= Cos^2theta×(sec^2theta)

=1/sec^theta ×sec^2theta

=1

LHS=RHS

( 1+tan^2theta= sec^2theta)

Cos^2theta= 1/sec^2theta)