Question

cosec theta +cot theta = 2 , then find sin theta​

Answer 1

Answer:

$\csc(theta) + \cot(theta) = 2 \\ = 1 \div \sin(theta) + \cot(theta) = 2 \\ = 1 \div \sin(theta) = 2 \div \cot(theta) \\ = \sin(theta) = \cot(theta) \div 2$

Step-by-step explanation:

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Answer 2

Answer:

$\frac{4}{5}$ is the required value of $sin\theta$

Step-by-step explanation:

Explanation:

Given , $cosec \theta + cot\theta$ = 2

If the binomial number is a + b, the conjugate is generated by altering the sign of one of the terms.

So (a + b ) and (a-b ) both are conjugate to each other .

Step 1:

We have $cosec\theta + cot \theta$ = 2 ........(i)

So , the conjugate of $cosec\theta + cot \theta$ is ($cosec\theta - cot \theta$)

Therefore , $cosec\theta - cot \theta = \frac{1}{2}$ ........(ii)

Adding (i) and (ii) we get ,

$(cosec\theta + cot \theta) + (cosec\theta - cot \theta )$ = $2 + \frac{1}{2}$

⇒$2cosec\theta = \frac{5}{2}$  ⇒$cosec \theta$ = $\frac{5}{2 }$×$\frac{1}{2}$ = $\frac{5}{4}$

As we know that , $sin\theta = \frac{1}{cosec\theta }$

⇒ $sin\theta = \frac{4}{5}$           [where $cosec \theta = \frac{5}{4}$]

Final answer:

Hence , $\frac{4}{5}$ is the value of $sin\theta$  .

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