Question

If sintheta+bcostheta=5,then (acostheta-bsintheta)*2 is equal to

Answer 1

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.