The value of the expression 2 sin6 theta cos6 theta 3 sin4 theta cos4 theta 1 is ........

Quantitative Aptitude (CGL) Trignometry

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The value of the expression 2(sin⁶θ+cos⁶θ)-3(sin⁴θ+cos⁴θ)+1 is

-1

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Explanation:

2(sin6θ+cos6θ)-3(sin4θ+cos4θ)+1
= 2{(sin²θ)³+(cos²θ)³}-3{(sin²θ)²+(cos²θ)²}+1
= 2{(sin²θ+cos²θ)³-3sin²θcos²θ(sin²θ+cos²θ)}-3{(sin²θ+cos²θ)²-2sin²θcos²θ}+1
=2(1-3sin²θcos²θ)-3(1-2sin²θcos²θ)+1
=2-6sin²θcos²θ-3+6sin²θcos²θ+1
=-1+1
=0