Question

question 5 (1 point)
the six addition and subtraction compound angle formulas may be used to create all equivalent double angle formulas for sine, cosine and tangent.
true
false

Explanation:

Step1: Recall addition and subtraction formulas

The addition formula for sine is \(\sin(A + B)=\sin A\cos B+\cos A\sin B\). Let \(A = B=\theta\), then \(\sin(2\theta)=\sin(\theta+\theta)=\sin\theta\cos\theta+\cos\theta\sin\theta = 2\sin\theta\cos\theta\).
The addition formula for cosine is \(\cos(A + B)=\cos A\cos B-\sin A\sin B\). Let \(A = B=\theta\), then \(\cos(2\theta)=\cos(\theta+\theta)=\cos^{2}\theta-\sin^{2}\theta\).
The addition formula for tangent is \(\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}\). Let \(A = B=\theta\), then \(\tan(2\theta)=\frac{\tan\theta+\tan\theta}{1-\tan\theta\tan\theta}=\frac{2\tan\theta}{1-\tan^{2}\theta}\).

Answer:

True