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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Prove that: (cos x + cos y)² + (sin x - sin y)² = 4cos²[(x + y) / 2]
Solution:
LHS = (cos x + cos y)2 + (sin x - sin y)2
= cos2x + cos2y + 2cos x cos y + sin2x + sin2y - 2sin x sin y [Because (a + b)² = a² + b² + 2ab and (a - b)² = a² + b² - 2ab ]
= 1 + 1 + 2cos (x + y) [Because cos2A + sin2A = 1 and cos (A + B) = cos A cos B - sin A sin B]
= 2 + 2cos (x + y)
= 2[1 + cos {2(x + y) / 2}]
= 2[1 + 2cos2{(x + y) / 2} - 1] [By double angle formulas, cos 2A = 2cos2A - 1]
= 4cos2[(x + y) / 2]
= RHS
NCERT Solutions Class 11 Maths Chapter 3 Exercise ME Question 3
Prove that: (cos x + cos y)² + (sin x - sin y)² = 4cos²[(x + y) / 2]
Summary:
We got, (cos x + cos y)2 + (sin x - sin y)2 = 4cos2[(x + y) / 2]. Hence Proved.
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