Prove the following identity: `costheta(t a ntheta+2)(2t a ntheta+1)=2s e ctheta+5sintheta`

Explanation

`\cos \theta[2 \tan ^{2} \theta+\tan \theta+4 \tan \theta+2]=2 \sec \theta+5 \sin \theta`
`\cos \theta[2(\sec ^{2} \theta-1)+5 \tan \theta+2][\tan ^{2}-\sec ^{2}-1]`
`\cos \theta[2 \sec ^{2} \theta-2+5 \tan \theta+2]`
`\cos \theta[\frac{2}{\cos ^{2} \theta}+5 \frac{\sin \theta}{\cos \theta}]`
`\operatorname{s\theta }[(\frac{1}{\cos \theta}[\frac{2}{\cos }+5 \sin ]].`
`2 \sec +5 \sin \theta=` R.H.S
Hence Proved.