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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.
A day full of math games & activities. Find one near you.
Prove that: 2cos π/13 cos 9π/13 + cos 3π/13 + cos 5π/13 = 0
Solution:
LHS = 2cos π/13 cos 9π/13 + [cos 3π/13 + cos 5π/13]
= 2cos π/13 cos 9π/13 + 2cos {(3π/13 + 5π/13) / 2} cos {(3π/13 - 5π/13) / 2} {Because cos A + cos B = 2cos [(A + B) / 2] cos [(A - B) / 2]}
= 2cos π/13 cos 9π/13 + 2cos 4π/13 cos (-π/13)
= 2cos π/13 cos 9π/13 + 2cos 4π/13 cos π/13 {Because cos (-x) = cos x}
= 2cos π/13(cos 9π/13 + cos 4π/13)
= 2cos π/13[2cos {(9π/13 + 4π/13) / 2} cos {(9π/13 - 4π/13) / 2}] {Because cos A + cos B = 2cos [(A + B) / 2] cos [(A - B) / 2]}
= 2cos π/13[2cos π/2 cos 5π/26]
= 2cos π/13 × 2 × 0 × cos 5π/26 [As cos π/2 = 0]
= 0
= RHS
NCERT Solutions Class 11 Maths Chapter 3 Exercise ME Question 1
Prove that: 2cos π/13 cos 9π/13 + cos 3π/13 + cos 5π/13 = 0
Summary:
We got, 2cos π/13 cos 9π/13 + cos 3π/13 + cos 5π/13 = 0. Hence Proved.
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