Posted by **Jen** on Friday, July 27, 2007 at 12:16am.

I need help with I just can't seem to get anywhere. this is as far as I have got:

Solve for b

arcsin(b)+ 2arctan(b)=pi

arcsin(b)=pi-2arctan(b)

b=sin(pi-2arctan(b))

Sub in Sin difference identity

let 2U=(2arctan(b))

sin(a-b)=sinacosb-cosasinb

=(sin(pi))(cos(2U))-(cos(pi))(sin(2U))

=(0)(cos(2U))-(-1)(sin(2U))

=(sin(2u))

b=sin(2arctan(b))

Now what should I do?

sin(2arctan(b))=

2 sin(arctan(b))cos(arctanb)

If you draw a right triangle with the lenghts of the two sides at right angles b and 1, so that one of the angeles becomes arctan(b), you see that

sin(arctan(b)) = b/sqrt[1+b^2]

cos(arctan(b)) = 1/sqrt[1+b^2]

## Answer This Question

## Related Questions

- tigonometry - expres the following as sums and differences of sines or cosines ...
- math - Eliminate the parameter (What does that mean?) and write a rectangular ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- algebra - Can someone please help me do this problem? That would be great! ...
- Trigonometry - Solve the equation for solutions in the interval 0<=theta<...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- calculus - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x...
- Calc. - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...

More Related Questions