If `alpha,beta,gamma,delta` are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity `k ,` then the value of `4sin(alpha/2)+3sin(beta/2)+2sin(gamma/2)+sin(delta/2)` is equal to (a)`2sqrt(1-k)` (b) `2sqrt(1+k)` (c)`(sqrt(1-k))/2` (d) none of these

Explanation

Here, it is given that ,

`alpha lt beta lt gamma lt delta`

`sinalpha = sinbeta = singamma = sin delta`

Now, `sinalpha = sin beta`

`=>sin(pi-alpha) = sin beta`

`=>pi-alpha = beta->(1)`

`sin alpha = singamma`

`=>sin(2pi+alpha) = gamma`

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