# Thread: Help with Compound Angle Formulae

1. ## Help with Compound Angle Formulae

Hi guys! How do you solve this question?

1. Tan 75° (using the compound angle formulae)

8. a) Develop formulas for cot(α + β) and cot(α - β).
b) Find cot 75° + cot 15° without using tables.

10. a) Develop formulas for the following.
i) tan 2α
ii) cot 2α

Thank you!

2. Originally Posted by finalfantasy
Hi guys! How do you solve this question?

1. Tan 75° (using the compound angle formulae)
recall that $\tan ( \alpha + \beta) = \frac {\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$

now, you can write $\tan 75$ as $\tan (45 +30 )$

now apply the formula

can you continue?

8. a) Develop formulas for cot(α + β) and cot(α - β).
b) Find cot 75° + cot 15° without using tables.
use the fact that $\cot ( \alpha + \beta ) = \frac {\cos ( \alpha + \beta) }{\sin ( \alpha + \beta)}$

you know the addition formulas for sine and cosine right?

10. a) Develop formulas for the following.
i) tan 2α
ii) cot 2α

Thank you!
again, write $\tan 2a$ as $\frac {\sin 2a}{\cos 2a}$

and $\cot 2a$ as $\frac {\cos 2a}{\sin 2a}$

and apply the double angle formulas for sine and cosine

3. hmm ... I tried doing tan (45 + 30) and attempted to solve it, but i kept getting the wrong answer!