Question

13. If sin theta= cosec theta and 0<theta<π, then the value of theta is ?​

Answer 1

Given data:

$sin\theta=cosec\theta$ and $0<\theta<\pi$

To find:

The value of $\theta$ in the given range

Step-by-step explanation:

Here $sin\theta=cosec\theta$

$\Rightarrow sin\theta=\dfrac{1}{sin\theta}$

$\Rightarrow sin^{2}\theta=1$

$\Rightarrow sin\theta=\pm 1$

Either $sin\theta=1$ or $sin\theta=-1$

$\Rightarrow \theta=\dfrac{\pi}{2}$ or $\theta=\dfrac{3\pi}{4}$

Since $0<\theta<\pi$, we say $\theta=\dfrac{\pi}{2}$

Answer:

The value of $\theta$ is $\dfrac{\pi}{2}$

Note:

We can solve the problem in another way.

$\quad sin^{2}\theta=1$

$\Rightarrow 1-sin^{2}\theta=0$

$\Rightarrow cos^{2}\theta=0$

$\Rightarrow cos\theta=0\quad [\because 0<\theta<\pi]$

$\Rightarrow cos\theta=cos\dfrac{\pi}{2}$

$\Rightarrow \theta=\dfrac{\pi}{2}$

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Answer 2

Answer:

see the answer below

Step-by-step explanation:

π/2