If cos theta sec theta 2 then the value of sin 6 theta cos 6 theta is ........

Quantitative Aptitude (CPO) Trignometry

If $$\cos \theta + \sec \theta = 2$$, then the value of $$\sin 6 \theta + \cos 6 \theta$$ is:

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SSC CPO 10th Nov 2022 Shift 3

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- Problem Summary: We need to find the value of $\sin 6\theta + \cos 6\theta$ given that $\cos \theta + \sec \theta = 2$.

- Simplification:

- From $\cos \theta + \frac{1}{\cos \theta} = 2$, simplify to find $\cos \theta = 1$.

- This implies $\theta = 0$ or $\theta = 2\pi$ (modulo $2\pi$).

- Calculate $\sin 6\theta + \cos 6\theta$:

- If $\theta = 0$, then $6\theta = 0$.

- $\sin 6\theta = \sin 0 = 0$ and $\cos 6\theta = \cos 0 = 1$.

- Thus, $\sin 6\theta + \cos 6\theta = 0 + 1 = 1$.

- Highlight Correct Answer:

- The correct option is Option 3: 1.

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