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

Simplify $\displaystyle\frac{\sec x-\cos x}{\tan x}$ into a single expression in terms of $\sin x$ and $\cos x$.

Given $\tan x+\sec x=k$, express $\sin x$ in terms of $k$.

Given $2\sin x + \sqrt{3}\cos x = 0$, solve for $\tan x$.

Express $\tan x$ in terms of $\sin x$ only, using $\cos x=\sqrt{1-\sin^2 x}$.

Simplify $\displaystyle\frac{1+\sin x}{\cos x}$ and show that it equals $\tan x+\sec x$.

Simplify $(\sec x+\tan x)(\sec x-\tan x)$ into a constant, expressing each function in terms of $\sin x$ and $\cos x$.

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

Express $\tan x$ in terms of $\sec x$ only by rearranging $1+\tan^2 x=\sec^2 x$.

Rearrange $1+\tan^2 x=\sec^2 x$ to express $\tan^2 x$ in terms of $\cos x$ only.

Simplify $\displaystyle\frac{\sin^2 x-\cos^2 x}{\sin x \cos x}$ to express it in terms of $\tan x$ and $\cot x$.

Express $\text{cosec } x$ in terms of $\sin x$ only.