Question

Prove that (sin 35 degree cos 55 degree + cos 35 degree sin 55 degree) +root 3 (tan 10 degree tan 30 degree tan 80 degree) =2

Answer 1

this is your proof hope it helps .

Answer 2

Answer:  Proved.

Step-by-step explanation:  We are given to prove the following:

$\sin 35^\circ\cos 55^\circ+\cos 35^\circ\sin 55^\circ+\sqrt3(\tan 10^\circ\tan 30^\circ\tan 80^\circ)=2.$

We will be using the following rules in the proof:

$(i)~\cos(90^\circ-\theta)=\sin \theta.\\(ii)`\sin(90^\circ-\theta)=\cos \theta.\\(iii)~\tan(90^\circ-\theta)=\cot \theta.$

We have

$L.H.S.\\\\=\sin 35^\circ\cos 55^\circ+\cos 35^\circ\sin 55^\circ+\sqrt3(\tan 10 ^\circ\tan 30^\circ\tan 80^\circ)\\\\=\sin 35^\circ\cos(90^\circ-35^\circ)+\cos 35^\circ\sin(90^\circ-35^\circ)+\sqrt 3\left(\tan 10^\circ\tan 30^\circ\tan(90^\circ-10^\circ)\right)\\\\=\sin^235^\circ+\cos^235^\circ+\sqrt3(\tan 10^\circ\tan 30^\circ\cot 10^\circ)\\\\=1+\sqrt3\left(\tan 10^\circ\times\dfrac{1}{\sqrt3}\times\dfrac{1}{\tan 10^\circ}\right)\\\\=1+1\\\\=2\\\\=R.H.S.$

Hence proved.