Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Trigonometry, Exercise 3: EXERCISE 3B

Solve the equation $2\tan \left(45°-x\right)=3\tan x$ for $0°⩽x⩽180°$.

Solve the equation $\sin \left(x+60°\right)=2\cos \left(x+45°\right)$  for $0°⩽x⩽180°$.

Solve the equation $\sin \left(x-45°\right)=2\cos \left(x+60°\right)$ for $0°⩽x⩽180°$.

Solve the equation $\tan \left(x+45°\right)=6\tan x$ for $0°⩽x⩽180°$.

Solve the equation $\cos \left(x+225°\right)=2\sin \left(x-60°\right)$ for $0°⩽x⩽180°$.

Solve the equation $\tan \left(x-45°\right)+\cot x=2$ for $0°⩽x⩽180°$.

Given that $\sin x+\sin y=p$ and $\cos x+\cos y=q$, find an expression for $\cos (x-y)$, in terms of $p$ and $q$.

Express each of the following as a single trigonometric ratio $2\sin 28°\cos 28°$