Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
- tan^2x + sec^2x = 1

Answer 1

first, use these identity :
- tan^2x = - sin^2 x/cos^2 x
sec^2 x = 1/cos^2 x

see ur equation can becomes
- tan^2x + sec^2x
= - sin^2 x/cos^2 x + 1/cos^2 x
= (- sin^2 x + 1)/cos^2 c
remember the identity that sin^2 x + cos^2 x = 1 or -sin^2 x + 1 = cos^2 x

so, it can be
= cos^2 x/cos^2 x
= 1

LHS = RHS

Answer 2

another way is if u remember the identity ;
sec^2 x = 1 + tan^2 x
so,
- tan^2x + sec^2x
= - tan^2x + 1 + tan^2 x
= 1

that's easier than before