Find the exact value in radian measure of each of the follow

Find the exact value, in radian measure, of each of the following: sin^-1 (- 1/2) arccos (- 1/Squareroot 2)

sin2x = tanx(1 +cos2x)

RHS : tanx(1 +cos2x) = tanx(2cos^2x)

= (sinx/cosx)(2cos^2x)

= 2sinx*cosx

= sin2x = LHS

6a) y = sin^-1(-1/2)

Range of sin^-1x : [ -pi/2 , pi/2]

So, siny = -1/2

y = -pi/6

b) y = arccos(-1/sqrt2)

Range of cos^-1x : [ 0 , pi]

cosy = -1/sqrt2

y = pi -pi/4 = 3pi/4