Question

If acostheta + bsintheta = m and asintheta - bcostheta = n then asq. + bsq.= ?
A) m + n
B) msq. - nsq.
C) msq. + nsq.
D) none of these

Answer 1

Answer :

Given that,

a cosθ + b sinθ = m ...(i)

a sinθ - b cosθ = n ...(ii)

Now, squaring and adding (i) and (ii), we get

(a cosθ + b sinθ)² + (a sinθ - b cosθ)²
= m² + n²

⇒ (a² cos²θ + 2 ab cosθ sinθ + b² sin²θ)
+ (a² sin²θ - 2 ab sinθ cosθ + b² cos²θ)
= m² + n²

⇒ (a² + b²) (cos²θ + sin²θ) = m² + n²

⇒ a² + b² = m² + n²

Thus, option (c) is correct.

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