Arctanx+Arcsinx=pi/2

I did this so far...
Arc sinx=pi/2-Arc tanx

x=sin (pi/2-Arctanx)

I did the sine expansion and it came out to cos(Arctanx)

then u=Arctanx

then x=1/(sqrt 1+x^2) (mutiply both sides by (sqrt 1+x^2) )
x(sqrt1+x^2)=1
x(sqrt1+x^2)-1=0

I don't know what to do now! The book has a problem similar (cosine instead of sine) but it comes out nicer because you can factor out an x... =0. Please help!

So far so good. All you need do now is a little light algbra. You have:


x \sqrt {1 + x^2} = 1


Square both sides, then rearrange:


x^2 (1 + x^2) = 1 \\
x^4 + x^2 - 1 = 0


Now, let w = x^2:

w^2 + w -1 = 0


Solve for w using the quadratic equation, then take the square root of that to find the value for x .

Post back and let us know what you get for a final answer.