If `3sintheta+5costheta=5,` then show that `5sintheta-3theta=+-3.`

Explanation

Given,
`3sintheta+5costheta=5 (i)`
Let `5sintheta-3costheta=x (ii)`
squaring and adding, we get
`(9sin^2theta+25cos^2theta+30sinthetacostheta)+(25sin^2theta+9cos^2theta-30sinthetacostheta)=25+x^2`
or `9(sin^2theta+cos^2theta)+25(sin^2theta+cos^2theta)=25+x^2`
or `34=25+x^2" or " x^2=9`
`or x=pm3`