Question

Cosec 39*cos51+tan 21*cot 69-sec21

Answer 1

cosec(90-51)cos51+tan21 tan(90-21)-sec21
=sec21 cos21+ tan21 cot21-sec21
=(1/cos21)*cos21+tan21*(1/tan21)-sec21
=1+1-sec21
=2-sec21

Answer 2

Answer:

$\csc 39\times cos 51+\tan21\times \cot 69-\sec^2 21=0$

Step-by-step explanation:

Given : Expression $\csc 39\times cos 51+\tan21\times \cot 69-\sec^2 21$

To find : Solve the expression ?

Solution :

Expression $\csc 39\times cos 51+\tan21\times \cot 69-\sec^2 21$

$=\csc (90-51)\times cos 51+\tan21\times \cot (90-21)-\sec^2 21$

$=\sec 51\times cos 51+\tan21\times \tan21-\sec^2 21$

$=\frac{1}{\cos 51}\times cos 51+\tan^2 21-\sec^2 21$

We know, $\tan^2\theta-\sec^2\theta=1$

$=1-1$

$=0$

Therefore, $\csc 39\times cos 51+\tan21\times \cot 69-\sec^2 21=0$