JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

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Application +4 | -1

0 < \theta < \pi

, then

\sqrt {2 + \,\,\sqrt {2\,\, + \sqrt {2\,\, + \ldots + \sqrt {2 + 2\,\,\cos \,\,\theta } } } }

there being n number of

\mathrm{2'}\,\mathrm{s}

is equal to

View answer and explanation

Correct option: A

2\,\,\cos \,\,\frac{\theta }{{{2^n}}}

Option A (

2\cos \frac{\theta}{{{{2^n}}}}

) is correct because it represents the simplified form of the nested square root expression after applying the identity

1 + \cos \theta = 2\cos^2 \frac{\theta}{2}

n times.

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