Show that sin1 x cos1 x pi2 Communication Skill Explain wh

Show that sin^-1 x + cos^-1 x = pi/2. (Communication Skill) Explain why sin^-1(sin 3pi/2) ne 3pi/2. (Computational Skill) Suppose f(x) = x+5/x-4. Find f^-1(x).

Solution

1. sin^-1x+ cos^-1x=pi/2

Starting with left side

sin^-1x+cos^-1x

Let sin^-1x=t

therefore sin t=x

and cos (90-t)=sin t

Therefore cos (90-t)=x

                   90-t=cos^-1x

Using this value of cos^-1x we get

t + 90-t =90 =pi/2 which is equal to right side

2. sin^-1(sin 3pi/2)

sin 3pi/2=-1

But it is not necessary that sin^-1-1 is equal to 3pi/2

3.f(x)=(x+5)/(x-4)

y= (x+5)/(x-4)

switching x and y

x= (y+5)/(y-4)

yx-4x=y+5

y(x-1)= 5+4x

y= (5+4x)/x-1

f^--1(x)= (5+4x)/(x-1)