If 2cos^4\theta – 2sin^4\theta = 4/ 3, then (2cos^2\theta + 1)is equal to

SSC CPO SI and ASI Model Paper 2

Question : 108 of 200

Marks: +1, -0

If $2cos^4θ – 2sin^4θ =$ $4/ 3$ , then $(2cos^2θ + 1)$ is equal to

Solution:

(3)

2cos4θ – 2sin4θ = 4/3

⇒ cos^4θ – sin^4 θ= 2/3

⇒ (cos^2θ – sin^2θ) (cos^2θ +sin^2θ) = 2/3

⇒ (cos^2θ – sin^2θ) = 2/3

⇒cos^2θ– 1 + cos^2θ= 2/3

⇒ 2 cos^2θ= 5/3

∴ (2cos^2θ + 1) = 5/3+1 = 8/3

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