if A COSA - B sine = C, Prove that
A sino + B cos ☺
+ a²+6²-C²
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Answer:squaring both sides,
... a² cos² x + b² sin² x - 2ab sin x cos x = c²
∴ a² ( 1 - sin² x ) + b² ( 1 - cos² x ) - 2ab sin x cos x = c²
∴ a² - a² sin² x + b² - b² cos² x - 2ab sin x cos x = c²
∴ a² + b² - c² = a² sin² x + b² cos² x + 2ab sin x cos x
∴ a² + b² - c² = ( a sin x + b cos x )²
∴ a sin x + b cos x = ± √( a² + b² - c²
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