Question

Sin theta = 1/4 when value of cos theta × cot theta × cosec theta

Answer 1

ANSWER:

Given:

• sin ө = 1/4

To Find:

• cos ө × cot ө × cosec ө

Solution:

We are given that,

$\implies\sin\theta=\dfrac{1}{4}$

We need to find the value of,

$\implies\cos\theta\times\cot\theta\times\csc\theta$

We know that

$\hookrightarrow\cot\theta=\dfrac{\cos\theta}{\sin\theta}$

And,

$\hookrightarrow\csc\theta=\dfrac{1}{\sin\theta}$

So,

$\implies\cos\theta\times\dfrac{\cos\theta}{\sin\theta}\times\dfrac{1}{\sin\theta}$

Cancelling cos ө,

$\implies\dfrac{1}{\sin^2\theta}$

So,

$\implies\dfrac{1}{(\sin\theta)^2}$

As, sin ө = 1/4,

$\implies\dfrac{1}{\left(\dfrac{1}{4}\right)^2}$

$\implies\dfrac{1}{\left(\dfrac{1}{16}\right)}$

So,

$\implies\dfrac{16}{1}$

Hence,

$\implies\bf cos\theta\times cot\theta\times cosec\theta=16$

Answer 2

Answer:

cos theta × cot theta × cosec theta = 16

Hope it helps!!

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