Exams › SSC CGL (Prelims) › General

If $\sin\theta+\cos\theta=p$, then find the value of $1+2\sin\theta\cos\theta$.

1. p
2. p^2
3. 2p
4. p+1

Correct answer: p^2

Solution

Squaring $\sin\theta+\cos\theta=p$ gives $p^2=\sin^2\theta+\cos^2\theta+2\sin\theta\cos\theta$. Since $\sin^2\theta+\cos^2\theta=1$, we get $p^2=1+2\sin\theta\cos\theta$. Hence the required value is $p^2$.

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