The value of \(\frac{cos^6θ + sin^6θ + 3sin^2θ cos^2θ}{cosec θ sec θ ( 1 - sin θ - cos θ) ( 1+ sin θ + cos θ)}\) is ?
Answer & explanation
Correct answer: option 2
Here,
⇒ cos6 θ + sin6 θ + 3sin2 cos2 θ
= cos6 θ + sin6 θ + 3sin2 cos2 θ (sin2 θ + cos2 θ)
= (cos2 θ + sin2 θ)3 = 1
Now,
= \(\frac{1}{cosec θ sec θ ( 1 - (sin θ + cos θ)(1 + (sin θ + cos θ)}\)
= \(\frac{1}{cosec θ sec θ (1^2 - (sinθ + cosθ)^2)}\)
= \(\frac{1}{cosec θ sec θ ( - 2sin θ cos θ) }\)
= - \(\frac{1}{2}\)