Without using a calwlator find the following sin1 sin3 pi co

Without using a calwlator find the following. sin^-1 [sin[-3 pi] cos [15^degree]

Solution

A. sin^-1[sin(-3pi)]

sin(-3pi) =0

So, sin^-1(0) = 0

B. cos15

use formula : cosx = sqrt[(1+cos2x)/2]

cos15 = sqrt[(1 +cos30)/2]

= sqrt[(1+ sqrt(3)/2)/2]

= sqrt(2+ sqrt3)/2