Question

\[ \text{If } \sin\theta+\cosec\theta=2, \]

\[ \text{then } \sin^2\theta+\cosec^2\theta \]

is equal to

(a) \(1\)
(b) \(4\)
(c) \(2\)
(d) none of these

Solution

Let

\[ x=\sin\theta \]

Then

\[ x+\frac1x=2 \]

Squaring both sides,

\[ \left(x+\frac1x\right)^2=4 \]

\[ x^2+\frac1{x^2}+2=4 \]

\[ x^2+\frac1{x^2}=2 \]

Therefore,

\[ \sin^2\theta+\cosec^2\theta=2 \]

Answer

\[ \boxed{2} \]

Correct Option: (c)