Prove the identity

1. Mar 25, 2016

Enochfoul

1. The problem statement, all variables and given/known data
Hi Everyone, Would somebody please be able able to check my working for the following problems:

(Q1) Prove the identity of cos3θ - cos7θ/sin 7θ + sin3θ ≡ tan 2θ
(Q2) Prove the identity of cos3θ ≡ 4 cos^3θ - 3 cos θ [hint: Express cos 3θ as cos (2θ+θ).]

2. Relevant equations

3. The attempt at a solution
Scanned working attached

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2. Mar 25, 2016

Ray Vickson

In Q1, do you mean
$$\cos 3 \theta - \frac{\cos 7 \theta}{\sin 7 \theta} + \sin 3 \theta$$
(as written), or do you mean
$$\frac{ \cos 3 \theta - \cos 7 \theta}{\sin 7 \theta + \sin 3 \theta} \:?$$

3. Mar 25, 2016

Enochfoul

Second one thanks

4. Mar 27, 2016

Enochfoul

Hi could anybody check my working please?

5. Mar 27, 2016

Staff: Mentor

Some helpers here at PF won't bother to look at work that is posted as an image or in an attached file. Work in this form makes it impossible to insert a comment at the location of an error, so you have to describe, in words, the location where things are going wrong.

Everything you did could have been posted directly in the text entry pane, using either the symbols available under the $\Sigma$ symbol on the menu bar, or by writing it in LaTeX. See Latex Primer under INFO --> Help/How-to menu.