If sintheta+bcostheta=5,then (acostheta-bsintheta)*2 is equal to
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Answer:
a² + b² - 25
Step-by-step explanation:
asinθ+bcosθ=5
Squaring on both sides
(asinθ+bcosθ)² = 25
a²Sin²θ + b²Cos²θ+2abSinθCosθ = 25
=> 2abSinθCosθ = 25 - (a²Sin²θ + b²Cos²θ)
Now
(aCosθ - bSinθ)² = a²Cos²θ+ b²Sin²θ - 2abCosθSinθ
= a²Cos²θ+ b²Sin²θ - 25 + (a²Sin²θ + b²Cos²θ)
= a²(Sin²θ+Cos²θ) + b²(Cos²θ+Sin²θ) - 25
= a² + b² - 25.
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