Question

Cos70 / sin20 + cos55 cosec35 / tan5 tan25 tan65 tan85=2

Answer 1

Answer:

Step-by-step explanation:Hope it will help you......

Answer 2

Step-by-step explanation:

Since we have given that

$\frac{\cos 70^\circ}{\sin 20^\circ}+\frac{\cos 55^\circ\times cosec\ 35^\circ}{\tan 5^\circ\times \tan 25^\circ\times \tan 65^\circ\times \tan 85^\circ}$

As we know that

$\cos(90^\circ-\theta)=\sin \theta\\\\and\\\\ \tan \theta\times \tan (90^\circ-\theta)=1$

So, it becomes ,

$=\frac{\cos (90^\circ-20^\circ)}{\sin 20^\circ}+\frac{\cos 55^\circ\times cosec\ (90^\circ-55^\circ)}{\tan 5^\circ\times \cot (90^\circ-5^\circ)\times \tan 65^\circ\times \tan (90-65^\circ)}\\\\=\frac{\sin 20^\circ}{\sin 20^\circ}+\frac{\cos 55^\circ\times sec\ 55^\circ}{\tan 5^\circ\times \cot 5^\circ\times \tan 65^\circ\times \cot 65^\circ}\\\\=1+1\\\\=2$

L.H.S. = R.H.S.

Hence , proved.