Question

evaluate tan 25 tan 65 - cot 25 cot 65​

Answer 1

Answer:

Tan 65/ cot 25

tan 65 can be written as

tan(90-65)/cot 25

cot 25/cot 25=1.

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Answer 2

The value of $\tan 25 \tan 65 - \cot 25 \cot 65$ = 0

Step-by-step explanation:

We have,

$\tan 25 \tan 65 - \cot 25 \cot 65$

To find, the value of $\tan 25 \tan 65 - \cot 25 \cot 65$ = ?

∴ $\tan 25 \tan 65 - \cot 25 \cot 65$

= $\tan 25 \tan (90-25) - \cot 25 \cot (90-25)$

Using the trigonometric identity,

$\tan (90 -A) = \cot A$ and  $\tan (90 -A) = \cot A$

= $\tan 25 \cot 25 - \cot 25 \tan 25$

Using the trigonometric identity,

$\tan A \cot A = 1$

= $\tan 25 \dfrac{1}{\tan 25} - \cot 25 \dfrac{1}{\cot 25 }$

= 1 - 1

= 0

∴ The value of $\tan 25 \tan 65 - \cot 25 \cot 65$ = 0