Question Type 3: Rearranging equations and simplifying equations into either sin or cos only Exercises

Express $\tan x \sec x$ in terms of $\sin x$ only.

Simplify $\displaystyle \frac{\sin x - \cos x}{\sin x + \cos x}$ by rationalizing the denominator and express in terms of $\sin x$ and $\cos x$ only.

Express $\tan x$ in terms of $\sin x$ and $\cos x$.

Simplify $(\tan^2 x + 1)\sin x\cos x$.

Simplify the expression $\displaystyle \frac{1}{1+\sin x} + \frac{1}{1-\sin x}$.

Express $\sec x$ in terms of $\sin x$ and $\cos x$.

Simplify $\sec x - \cos x$ into an expression involving only $\sin x$ and $\cos x$ (no $\sec$).

Simplify $\displaystyle \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}$ into a single fraction in terms of $\sin x$ and $\cos x$.

Simplify $\displaystyle \frac{1 - \sin^2 x}{\cos x}$ into either $\sin x$ or $\cos x$ only.

Simplify $\tan x + \cot x$ into a single fraction in terms of $\sin x$ and $\cos x$.

Simplify $\displaystyle \frac{\tan x}{1 + \tan^2 x}$ into an expression in $\sin x$ and $\cos x$ only.

Simplify $\displaystyle \frac{\sin^3 x + \sin x\cos^2 x}{\sin x}$ into a simpler expression in $\sin x$ and $\cos x$ only.