JEE Class main Answered
Cos66+sin84
Asked by veerababukoppisettiveerababu3 | 17 Apr, 2024, 17:49: PM
Expert Answer
Let α = Cos66 + sin84 = cos(60+6) + sin(90-6)
α = [ cos60 cos6 - sin60 sin 6] + [sin90 cos6 - cos90 sin6 ]
since cos90 = 0 and sin90 = 1 , then we get
α = [ cos60 cos6 - sin60 sin 6] + [ cos6 ]
α = [ (3/2) cos6 - (√3/2) sin 6]
α = √3 [ (√3/2) cos6 - (1/2) sin 6]
α = √3 [ sin60 cos6 - cos60 sin6]
α = √3 sin(60-6) = √3 sin54 = 1.401
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