Question

Cot 10 *tan 15 *tan 45*tan 75*cot 80 =1

Answer 1

Step-by-step explanation:

cot80*cot10*tan75* tan15*tan45 =1

cot80*cot(90-80)*tan75*tan(90-75)*tan45 =1

{cot 80 *tan 80*tan75* cot75 *tan45 =1

cot80×1/cot80*tan75×1/tan75*tan45 =1

tan 45=1

therefore

1×1×1=1

1=1

LHS=RHS

Answer 2

$\cot 10 \tan 15 \tan 45\tan 75\cot 80=1$, proved.

Step-by-step explanation:

L.H.S.=$\cot 10 \tan 15 \tan 45\tan 75\cot 80$

$=\cot 10 \tan 15 \tan 45\tan (90-15)\cot (90-10)$

$=\cot 10 \tan 15 \tan 45\cot 15\tan 10$

[ ∵ $\tan (90-\theta)=\cot \theta and \cot (90-\theta)=\tan \theta$]

$=(\cot 10 \tan 10) \tan 45(\tan 15\cot 15)$

$=(1) \tan 45(1)$

$=1$ [∵ $\tan 45=1$]

=R.H.S.

Hence, $\cot 10 \tan 15 \tan 45\tan 75\cot 80=1$, proved.