Question

evaluate cot 46 degree cot 18 degree cot 44 degree cot 72 degree​

Answer 1

Answer:

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Answer 2

The value of $\cot 46\cot 18\cot 44 \cot 72$ is equal to 1.

Step-by-step explanation:

We have,

$\cot 46\cot 18\cot 44 \cot 72$

To find, the value of $\cot 46\cot 18\cot 44 \cot 72$ = ?

∴ $\cot 46\cot 18\cot 44 \cot 72$

$=\cot 46\cot 18\cot (90-46) \cot (90-18)$

Using the trigonometric identity,

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

$=\cot 46\cot 18\tan 46 \tan 18$

$=(\cot 46\tan 46)(\cot 18 \tan 18)$

$=(\cot 46.\dfrac{1}{\cot 46} )(\cot 18.\dfrac{1}{\cot 18} )$

Using the trigonometric identity,

$\cot A\tan A=1$

⇒ $\tan A=\dfrac{1}{\cot A}$

= 1 × 1

= 1

∴ The value of $\cot 46\cot 18\cot 44 \cot 72$ = 1

Thus, the value of $\cot 46\cot 18\cot 44 \cot 72$ is equal to 1.