यदि `alpha = tan^(-1)(1/2)+tan^(-1)(1/3)`,
` beta = cos^(-1)(2/3)+cos^(-1)(sqrt5/3)`
तथा `gamma = sin^(-1)[sin.((2pi)/3)]+1/2 cos^(-1)[cos((2pi)/3)]`
यदि `4(sin^(2) alpha + sin^(2) beta + sin^(2) gamma) = a^(2)` है , तब a बराबर होगा

Options

A. `pm 1`
B. `pm 2`
C. `pm 3`
D. इनमें से कोई नहीं

Answer

C

Explanation

`:' 4(sin^(2) alpha+ sin^(2) beta+ sin^(2) gamma) = a^(2)`
` rArr 4( sin^(2). pi/4+sin^(2). pi/2 + sin^(2). (2pi)/3) = a^(3)`
` rArr 4(1/2 + 1 + 3/4) = a^(2)`
` rArr a^(2) = 4 xx 9/4 rArr a^(2) = 9 rArr a = pm 3`