The expression $(cos^6\theta +sin^6\theta -1) (tan^2\theta +cot^2\theta +2)+1$ is equal to :
Answer & explanation
Correct answer: option 2
(cos6θ + sin6θ - 1 ) ( tan2θ + cot2θ + 2 ) + 1
Put θ = 30º
= ( (\(\frac{√3}{2}\))6 + (\(\frac{1}{2}\))6 - 1 ) ( (\(\frac{1}{√3}\))2 + (√3)2 + 2 ) + 1
= ( \(\frac{27}{64}\) + \(\frac{1}{64}\) - 1 ) ( \(\frac{1}{3}\) + 3 + 2 ) + 1
= ( -\(\frac{36}{64}\) ) ( \(\frac{16}{3}\) + 1
= -2