Question

(i) $si{n}^6\theta +co{s}^6\theta =1-3si{n}^2\theta co{s}^2\theta$

(ii) $si{n}^4\theta -co{s}^4\theta =si{n}^2\theta -co{s}^2\theta$

(iii) $cose{c}^4\theta -cose{c}^2\theta =co{t}^4\theta +co{t}^2\theta$

Answer 1

(ii) $si{n}^4\theta -co{s}^4\theta =si{n}^2\theta -co{s}^2\theta LHS=si{n}^4\theta -co{s}^4\theta =(si{n}^2\theta {)}^2-(co{s}^2\theta {)}^2=(si{n}^2\theta +co{s}^2\theta )(si{n}^2\theta -co{s}^2\theta )=si{n}^2\theta -co{s}^2\theta =RHS$

(iii)$cose{c}^4\theta -co{t}^4\theta =cose{c}^2\theta +co{t}^2\theta LHS=cose{c}^4\theta -co{t}^4\theta =(cose{c}^2\theta {)}^2-(co{t}^2\theta {)}^2=(cose{c}^2\theta +co{t}^2\theta )(cose{c}^2\theta -co{t}^2\theta )=cose{c}^2\theta +co{t}^2\theta =RHS$