For any $\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$, the expression $3{(\cos \theta - \sin \theta )^4}$$ + 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta $ equals :

Question

For any $\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$, the expression

$3{(\cos \theta - \sin \theta )^4}$$ + 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta $

equals :

13 – 4 cos²$\theta $ + 6sin²$\theta $cos²$\theta $

13 – 4 cos⁶$\theta $

13 – 4 cos²$\theta $ + 6cos²$\theta $

13 – 4 cos⁴$\theta $ + 2sin²$\theta $cos²$\theta $

Solution

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