D1.5

prove simple trigonometric identities, using the Pythagorean identity ${\sin }^{2}x+{\cos }^{2}x=1$; the quotient identity $\tan x=\frac{\sin x}{\cos x}$; and the reciprocal identities $\sec x=\frac{1}{\cos x}$, $\csc x=\frac{1}{\sin x}$, and $\cot x=\frac{1}{\tan x}$ Sample problem: Prove that $1-{\cos }^{2}x=\sin x\cos x\tan x$.