Evaluate arcsin cot pi4 tan sin1 513Solutiona arcsin cotpi4

Evaluate: arcsin [cot (- pi/4)) tan [sin^-1 (-5/13)]

Solution

a) arcsin[ cot(-pi/4)]

cot(-pi/4) = -1

arcsin[-1] = -pi/2

b) tan[ sin^-1(-5/13)]

let y = sin^-1(-5/13)

siny = -5/13 ----> tany = -5/12

So, tan[ sin^-1(-5/13)] = tany = -5/12

c) tan( arccos(x/2) )

Let arccos(x/2) =y

cosy = x/2

So, tany = sqrt( 4-x^2)/x

tan( arccos(x/2) ) = tany =  sqrt( 4-x^2)/x