Question

If cos(alpha - beta ) = 1/2, cos(alpha+beta) = 0, the sin (alpha+ 5beta) Sin(5alpha+beta) =

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\cos( \alpha - \beta ) = \frac{1}{2} = \cos(60)$

$\alpha - \beta = 60.....(i)$

$\cos( \alpha + \beta ) = 0 = \cos(90)$

$\alpha + \beta = 90......(ii)$

Apply (i) + (ii)....

$2 \alpha = 60 + 90 = 150$

$\alpha = 75 \: \: \: and \: \: \beta = 15$

So,

$\sin( \alpha + 5 \beta ) \times \sin(5 \alpha + \beta ) = \sin(75 + 5 \times 15) \sin(5 \times 75 + 15) = \sin(150) \sin(390) = \sin(180 - 30) \sin(360 + 30) = \sin(30) \sin(30) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \: \: ans.$

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