IB Mathematics Applications & Interpretation 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 $\frac{\sin x-\cos x}{\sin x+\cos x}$ 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 $\frac{1}{1+\sin x}+\frac{1}{1-\sin x}$.

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

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

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