Question

If `sintheta+sin^2theta=1` Prove that `cos^2theta+cos^4theta=1`

Answer 1

` sin theta + sin^(2)theta =1 `
`rArr sin theta= 1- sin^(2)theta `
`rArr sin theta = cos^(2)theta " " [because 1- sin^(2)theta = cos^(2)theta] `
`rArr sin^(2)theta = cos^(4)theta `
`rArr 1- cos^(2)theta =cos^(4)theta " " [because sin^(2)theta = 1- cos^(2)theta] `
`rArr cos^(2)theta +cos^(4) theta =1. `
Hence, ` cos^(2)theta + cos^(4)theta =1. `