4arcsinx + arccosx =pi then x=??

Question

#4arcsinx + arccosx =pi#

6018 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-30T16:00:41

# x=1/2#.

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#.

Answer 2 · 2018-06-30T16:15:48

Please see below.

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#