Question

solve cot^-1(cot(-pi/8)) without a calculator??

Answer 1

Cot( x/2)=cos(x/2) / sin(x/2)

= sqr(1+cosx)/sqr(1-cosx)

=sinx/(1-cosx)

So cot (pi/8)= sin (pi/4) / [1-cos(pi/4)]

=(sqr2)/2 / [1-(sqr2)/2]

=sqr2/(2-sqr2)

Sqr2(2+sqr2)/2

= (2sqr2+2)/2

= sqr2+1