Exams › SSC CGL (Prelims) › General

If $\cos\theta=-\frac{4}{5}$ and $\theta$ lies in the third quadrant, calculate the value of $(\sin\theta+\cos\theta)^2$.

1. $\frac{1}{25}$
2. $\frac{7}{5}$
3. 1
4. $\frac{49}{25}$

Correct answer: $\frac{49}{25}$

Solution

Given $\cos\theta=-\frac{4}{5}$ and $\theta$ is in the third quadrant, $\sin\theta$ is also negative. Using $\sin^2\theta=1-\cos^2\theta=1-\frac{16}{25}=\frac{9}{25}$, we get $\sin\theta=-\frac{3}{5}$. Then $(\sin\theta+\cos\theta)^2=\left(-\frac{3}{5}-\frac{4}{5}\right)^2=\left(-\frac{7}{5}\right)^2=\frac{49}{25}$.

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