Question
If sinθ +cos θ = √7/2, then find the value of sinθ
– cosθ.Solution
sinθ + cos θ = √7/2, Squaring both sides. ⇒ sin2θ + cos2θ + 2sinθ.cosθ = 7/4 ⇒ 1 + 2sinθ.cosθ = 7/4 ⇒ sinθ.cosθ = 3/8 We can write; sin2θ + cos2θ = (sinθ – cosθ)2 + 2sinθ.cosθ ⇒ (sinθ – cosθ)2 = 1 – 3/4 = 1/4 ⇒ (sinθ – cosθ) = 1/2
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