question 1 (1 point)\nthe six addition and subtraction compound angle formulas may be used to create all…

Brief Explanations:

The double - angle formulas for sine ((\sin2\alpha = 2\sin\alpha\cos\alpha)), cosine ((\cos2\alpha=\cos^{2}\alpha-\sin^{2}\alpha = 2\cos^{2}\alpha - 1=1 - 2\sin^{2}\alpha)) and tangent ((\tan2\alpha=\frac{2\tan\alpha}{1 - \tan^{2}\alpha})) can be derived from the addition formulas. For example, using the formula (\sin(A + B)=\sin A\cos B+\cos A\sin B), when (A = B=\alpha), we get (\sin2\alpha=\sin(\alpha+\alpha)=\sin\alpha\cos\alpha+\cos\alpha\sin\alpha = 2\sin\alpha\cos\alpha). Similarly, for cosine (\cos(A + B)=\cos A\cos B-\sin A\sin B), when (A = B=\alpha), (\cos2\alpha=\cos(\alpha+\alpha)=\cos\alpha\cos\alpha-\sin\alpha\sin\alpha=\cos^{2}\alpha-\sin^{2}\alpha). And for tangent (\tan(A + B)=\frac{\tan A+\tan B}{1-\tan A\tan B}), when (A = B=\alpha), (\tan2\alpha=\frac{\tan\alpha+\tan\alpha}{1-\tan\alpha\tan\alpha}=\frac{2\tan\alpha}{1 - \tan^{2}\alpha}).

Answer:

True