IB Mathematics Analysis and Approaches Question Type 3: Rearranging Equations and Simplifying Equations Into Either Sin or Cos Only Exercises

Simplify $\frac{\sec x-\cos x}{\tan x}$ 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 $\frac{1+\sin x}{\cos x}$ 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 $\frac{{\sin }^{2}x-{\cos }^{2}x}{\sin x\cos x}$ to express it in terms of $\tan x$ and $\cot x$.

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