Question

1 + tan squA =sec squ A​

Answer 1

$\huge \bold{hey \: there}$

To prove:

(1+tan²A)=sec²A

We know that tanA=sinA/CosA

So, tan²A= sin²A/cos²A

LHS:

=1+sin²A/cos²A

=cos²A+sin²A/cos²A

=sin²A+cos²A/cos²A

We have an identity: sin²A+cos²A=1, therefore

=1/cos²A

Now, 1/cosA= secA; 1/cos²A= sec²A

= sec²A

LHS= RHS

Hence proved.