The value of the expression 2 (\sin^6\theta + \cos^6\theta) –3 (\sin^4\theta + \cos^4\theta) + 1 is

SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 89 of 100

Marks: +1, -0

The value of the expression

2 (sin^6θ + cos^6θ) –3 (sin^4θ + cos^4θ) + 1

Solution:

(2)

2 (sin^6θ + cos^6θ) –3 (sin^4θ + cos^4θ) + 1

=2 { (\sin ^{2} \θ+\cos ^{2} \θ)^{3}-3 \sin ^{2} \θ \cos ^{2} \θ(\sin ^{2}\θ+\cos ^{2} \θ) }

-3 { (\sin ^{2} \θ +\cos ^{2} \θ )^{2}-2 \sin ^{2} \θ. \cos ^{2}\θ}+1

=2 (1-3 \sin ^{2} \θ. \cos ^{2} \θ)-3(1- 2 \sin ^{2} \θ.\cos ^{2} \θ)+1

=2-6 \sin ^{2} \θ. \cos ^{2} \θ-3+6 \sin ^{2} \θ. \cos ^{2} \θ+1

=3-3=0

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