Question
If x = 4 cos A + 5 sin A snd y = 4 sin A – 5 cos
A, then the value of x2+y2 is :Solution
X = 4 cos A + 5 sin A y = 4 sin A − 5 cos A x 2 + y2 = (4 cos A + 5 sin A)2 + (4 sin A − 5 cos A)2 ((a + b)2 = a2 + b2 + 2ab) = (16cos2A+25sin2A +40 cos Asin A)+(16 sin2A +25cos2A− 40cosA sin A )2 (sin2A+ cos2A=1) =16+25=41
15Â Â Â Â Â Â Â Â Â Â 15Â Â Â Â Â Â Â Â Â Â 60Â Â Â Â Â Â Â Â Â Â 540Â Â Â Â Â Â Â Â 8650
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