If cos ⁡ - sin ⁡ = 5 sin ⁡ , then cos ⁡ +4 sin ⁡ =

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Correct answer: D. (d) cos ⁡ - sin ⁡ = 5 sin ⁡ 5 ( cos ⁡ - sin ⁡ )^2= ( 5 sin ⁡ )^2 cos^2 ⁡ + sin^2 ⁡ -2 sin ⁡ θcos ⁡ =5 sin^2 ⁡ 1-2 sin ⁡ θcos ⁡ =5 sin^2 ⁡ 1-5 sin ⁡2=2 sin ⁡ θcos ⁡ Now , ( cos ⁡ +4 sin ⁡ )^2= cos^2 ⁡ +16 sin^2 ⁡ +4.2 sin ⁡ θcos ⁡ = cos^2 ⁡ +16 sin^2 ⁡ +(1-5 sin^2 ⁡ ) = cos^2 ⁡ +16 sin^2 ⁡ +4-20 sin^2 ⁡ = cos^2 ⁡ -4 sin^2 ⁡ +4= cos^2 ⁡ +4(1- sin^2 ⁡ ) = cos^2 ⁡ +4 cos^2 ⁡ =5 cos^2 ⁡ ∴ cos ⁡ +4 sin ⁡ = 5 cos^2 ⁡ = 5 cos ⁡

$If cos θ - sin θ = 5 sin θ, then cos θ + 4 sin θ =$

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