Trigonometry - compound angels

[Michael_Light]

Homework Statement

Evaluate http://img828.imageshack.us/img828/3383/msp588119g042f0f3ba0368.gif without using calculator or tables.

Homework Equations

The Attempt at a Solution

I have no ideas how tan37 and tan23 can be found... can anyone give me some hints? The answer given is √3. Thank you...

 

[mege]

I don't think you're meant to evaluate tan 37 and tan 23 directly, but do you know any identities which may be used? Like any sum of sin or cos rules? Hint: break tan down into it's sin and cos parts.

(37+23 = 60, and I'd wager you know the sin cos and tan of 60)

 

[eumyang]

Actually, I don't think you need to express tangent in terms of sine and cosine. Just use the tangent of a sum identity.

Given
$$\tan (a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}$$

solve for "tan a + tan b".

 

[Mark44]

Compound "angels" huh?

You know, of course, that there's a difference between an angel and an angle?