Question

2 (cos 65 / sin 25 ) - ( tan 20 / cot 70 ) - sin 90 + tan 35 + tan 60 +tan 55 * tan 85 .

Answer 1

The answer is attached below

Answer 2

$2\dfrac{\cos 65}{\sin 25}-\dfrac{\tan 20}{\cot 70}-\sin 90+\tan 5.\tan35.\tan 60.\tan 55.\tan 85=\sqrt{3}$

Step-by-step explanation:

We have,

$2\dfrac{\cos 65}{\sin 25}-\dfrac{\tan 20}{\cot 70}-\sin 90+\tan 5.\tan35.\tan 60.\tan 55.\tan 85$

To find, $2\dfrac{\cos 65}{\sin 25}-\dfrac{\tan 20}{\cot 70}-\sin 90+\tan 5.\tan35.\tan 60.\tan 55.\tan 85=?$

∴ $2\dfrac{\cos 65}{\sin 25}-\dfrac{\tan 20}{\cot 70}-\sin 90+\tan 5.\tan35.\tan 60.\tan 55.\tan 85$

=$2\dfrac{\cos (90-25)}{\sin 25}-\dfrac{\tan (90-70)}{\cot 70}-1+\tan 5.\tan35.\tan 60.\tan (90-35).\tan (90-5)$

$=2\dfrac{\sin 25}{\sin 25}-\dfrac{\cot 70}{\cot 70}-1+\tan 5.\tan35.\tan 60.\cot 35.\cot 5$

$=2-1-1+\tan 60=\tan 60$

=$\sqrt{3}$

Hence, $2\dfrac{\cos 65}{\sin 25}-\dfrac{\tan 20}{\cot 70}-\sin 90+\tan 5.\tan35.\tan 60.\tan 55.\tan 85=\sqrt{3}$

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