यदि ` sin A sin (60^(@) -A) sin (60^(@) +A) = k sin 3A` हो, तो `k` किसके बराबर है ?

Options

A. `1/4`
B. `1/2`
C. `1`
D. `4`

Answer

A

Explanation

दिया है , ` sin A [ sin^(@) 60^(@)- sin^(2) A] = k sin 3A `
` [ :' sin(A+B) *sin (A-B)`
` = sin^(@) A-sin^(2)B]`
` rArr sinA [ 3/4 -sin ^(2) A] = k sin 3A`
` rArr sin3A - 4 sin^(3) A = 4 k sin3A`
` rArr sin 3A = 4 k sin 3 A`
` rArr = 4k`
` rArr k = 1/4`