## anonymous 4 years ago hey what is tan(45+a) equal to?

1. anonymous

how does this (1 - tan^2a)/(1+tan^2a) cos 2a?

2. anonymous

(1 - tan^2a)/(1+tan^2a) = cos 2a?

3. anonymous

$\tan (a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}$ Hmm that's the formula. One thing you can do is use this $$\large \tan a = \frac{\sin a}{\cos a}$$ $\frac{1 - \frac{\sin^2a}{\cos^2a}}{1 + \frac{\sin^2a}{\cos^2a}}$I hope you can do the algebra from here.

4. anonymous

ishaan do we expand the 1 into sin^2a +cos^2a?

5. anonymous

yeah! :-D

6. anonymous

can you expand this out cause i don't really get it

7. anonymous

okay, i will try. $\large \frac{\frac{cos^2a - \sin^2a}{\cos^2a}}{\frac{\cos^2a+\sin^2a}{\cos^2a}}$ $\Large \frac{\frac{cos^2a - \sin^2a}{\cancel\cos^2a}}{\frac{1}{\cancel \cos^2a}}$ $\cos^2a - \sin^2a = \cos 2a$

8. anonymous

oh i see thank you very much

9. anonymous

no problem

10. anonymous

hey ishaan don't we get 2cos2a then and not 2/cos2a

11. anonymous

no i think you forgot the real equation it's $$2 \frac{1 +tan^2a}{1 - tan^2a}$$