Question

Prove that $2se{c}^2\theta -se{c}^4\theta -2cose{c}^2\theta +cose{c}^4\theta -ta{n}^4\theta$ [3 MARKS]

Answer 1

Formula: 1 Mark
Proof: 2 Marks


$RHS=co{t}^4\theta -ta{n}^4\theta =(co{t}^2\theta {)}^2-(ta{n}^2\theta {)}^2=(cose{c}^2\theta -1{)}^2-(se{c}^2\theta -1{)}^2=cose{c}^4\theta +1-2cose{c}^2\theta -(se{c}^4\theta +1-2se{c}^2\theta )=cose{c}^4\theta +1-2cose{c}^2\theta -se{c}^4\theta -1+2se{c}^2\theta =2se{c}^2\theta -se{c}^4\theta -2cose{c}^2\theta +cose{c}^4\theta =LHS$