Question

if ` 3 sin theta + 5 costheta = 5` then prove that `5sintheta- 3costheta` = `| 3|`

Answer 1

We have ,
`3costheta-5sintheta=3`
Squaring both sides,
`(3costheta-5sintheta)^(2)=9`
`rArr9cos^(2)theta+25sin^(2)theta-30sinthetacostheta=9`
`rArr9(1-sin^(2)theta)+25(1-cos^(2)theta)-30sinthetacostheta=9`
`9sin^(2)theta+25cos^(2)theta+30sinthetacostheta=9+25-9`
`rArr(3sin^(2)theta+5costheta)^(2)=25`
`:. 3sintheta+5costheta=5`
(taking positive sign as `sinthetaandcostheta`both are positive in I quadrant)