Choose the correct answer. If +cosec =2, then ^2 +cosec^2 is equa… - Vidyadip

MCQ

Choose the correct answer.

If $\sin\theta+\text{cosec}\theta=2,$ then $\sin^2\theta+\text{cosec}^2\theta$ is equal to:

A
1
B
4
C
2
D
None of these

✓

Answer

2

Solution:

$\sin\theta+\text{cosec}\theta=2$

$\Rightarrow\sin\theta+\frac{1}{\sin\theta}=2$

$\Rightarrow\sin^2\theta+1=2\sin\theta\Rightarrow(\sin\theta-1)^2=0\Rightarrow\sin\theta=1$

$\therefore\sin^2\theta+\text{cosec}^2\theta=1+1=2$

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