Question

what is the value of cot( 45+ x)×cot (45-x)​

Answer 1

Answer:

Value of cot(45+x)×cot(45-x)=1

Step-by-step explanation:

Value of cot(45+x)×cot(45-x)

= cot(45+x)× cot[90-(45+x)]

= cot(45+x) × tan(45+x)

= 1

Therefore,

Value of cot(45+x)×cot(45-x)=1

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Answer 2

The value of $\cot(45+x)\times \cot(45-x)$ is 1.

Step-by-step explanation:

We need to find the value of $\cot(45+x)\times \cot(45-x)$. We know that,

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

So,

$=\cot(45+x)\times \cot(45-x)\\\\=\cot(45+x)\times \cot(90-(45-x))\\\\=\cot(45+x)\times \tan(45+x)$

Since, $\cot\theta=\dfrac{1}{\tan\theta}$

It implies,

$\cot(45+x)\times \cot(45-x)=1$

So, the value of $\cot(45+x)\times \cot(45-x)$ is 1.

Learn more,

Trigonometry

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