Need Help Proving Identities for Q1 and Q2 in Trigonometry

[Enochfoul]

Homework Statement

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).]

Homework Equations

The Attempt at a Solution

Scanned working attached

 

[Ray Vickson]

Homework Statement

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).]

Homework Equations

The Attempt at a Solution

Scanned working attached

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

 

[Enochfoul]

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

Second one thanks

 

[Enochfoul]

Hi could anybody check my working please?

 

[Mark44]

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