find value of x, without using calculator or table

Question

anonymous · Answer

$$\tan ^{-1} \frac{ 1 }{ 2 } - \tan^{-1}\frac{ 1 }{ 3 } = \sin^{-1} x$$

tkhunny · Answer

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I strongly suggest you become acquainted with Right Triangles.

tkhunny · Answer

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Are we getting anywhere?

anonymous · Answer

im Googling the right triangle

tkhunny · Answer

Why not rewrite your equation in terms of the A and B I created?

anonymous · Answer

yeah, then apply the sum of tan right?

anonymous · Answer

i mean tan (A-B)

tkhunny · Answer

I'd use the sine of the difference.  This will also expose the 'x' on the other side.

anonymous · Answer

i see, i'll try first

anonymous · Answer

i got $$\frac{ \sqrt{2} }{ 10 } = \sin ^{-1} x$$

anonymous · Answer

but the answer is √2 /10

tkhunny · Answer

You cannot possibly get that.

$\sin(A - B) = \sin(\sin^{-1}(x))$

Go ahead and write things out.  The notation can help you.

$\sin(A)\cos(B) - \cos(B)\sin(A) = x$

What do you get for those four values on the left?

anonymous · Answer

i get $$\frac{ \sqrt{2} }{ 10 }$$

anonymous · Answer

i got it, thanks