The value of $\sec ^4 \theta\left(1-\sin ^4 \theta\right)-2 \tan ^2 \theta$ is:
Answer & explanation
Correct answer: option 2
sec4 θ ( 1 - sin4 θ ) - 2 tan²θ
\(\frac{1 }{cos4 θ}\)× ( 1 - sin² θ ) × ( 1 + sin² θ ) - 2 tan²θ
{ using , sin² θ + cos² θ = 1 }
= \(\frac{1 }{cos4 θ}\)× ( cos² θ ) × ( 1 + sin² θ ) - 2 tan²θ
= \(\frac{1 }{cos² θ}\) × ( 1 + sin² θ ) - 2\(\frac{sin² θ }{cos² θ}\)
= \(\frac{1 + sin² θ - 2 sin² θ }{cos² θ}\)
= \(\frac{1 - sin² θ }{cos² θ}\)
= \(\frac{cos² θ }{cos² θ}\)
= 1