4arcsinx + arccosx =pi then x=??

4arcsinx + arccosx =pi

2 Answers
Jun 30, 2018

x=1/2.

Explanation:

We know that, arcsinx+arccosx=pi/2.

:. arccosx=pi/2-arcsinx.

Subst.ing in the given eqn. we get,

4arcsinx+(pi/2-arcsinx)=pi.

:. 3arcsinx=pi-pi/2=pi/2.

:. arcsinx=pi/6.

:. x=sin(pi/6)=1/2.

This also satisfy the given eqn.

:."The soln. is "x=1/2.

Jun 30, 2018

Please see below.

Explanation:

First note that rarrsin^(-1)x+cos^(-1)x=pi/2

Now given equation is,

rarr4sin^(-1)x+cos^(-1)x=pi

rarr3sin^(-1)x+sin^(-1)x+cos^(-1)x=pi

rarr3sin^(-1)x+pi/2=pi

rarr3sin^(-1)x=pi-pi/2=pi/2

rarrsin^(-1)x=pi/6

rarrx=sin(pi/6)=1/2