If sinθ + cosθ = √7/2, then what is sinθ – cosθ equal to?
If sinθ + cosθ = √7/2, then what is sinθ – cosθ equal to? Correct Answer 1/2
sinθ + cosθ = √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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Feb 20, 2025