If sinθ + cosθ = √3/2, and θ is an acute angle, find the value of sin²θ + cos²θ - 2sinθcosθ.
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Correct answer: C
Explanation
given :
sinθ + cosθ = √3/2
θ is an acute angle
(sinθ + cosθ)² = sin²θ + cos²θ + 2sinθcosθ
(√3/2)² = 1 + 2sinθcosθ
3/4 = 1 + 2sinθcosθ
2sinθcosθ = 3/4 − 1
2sinθcosθ = −1/4
sin²θ + cos²θ − 2sinθcosθ
= 1 − (−1/4)
= 5/4