If 1 + sin2 θ = a cos2 θ , then find sec4 θ - tan4 θ.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. a.
1 + sin2θ = a cos2θ
sec4θ - tan4θ = (sec2θ + tan2θ)(sec2θ - tan2θ)
= (sec2θ + tan2θ)
= (1/cos2θ + sin2θ/cos2θ)
= (1 + sin2θ)/cos2θ
= (a cos2θ)/cos2θ
= a