$\cos \,\,2{\rm{\theta }} + 2\,\,\cos \,\,{\rm{\theta \;}}$ is always

Less than or equal to $\frac{3}{2}$

JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Easy

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Analyzing +4 | -1

\cos \,\,2\mathrm{\theta } + 2\,\,\cos \,\,\mathrm{\theta \;}

is always

View answer and explanation

Correct option: C

Greater than or equal to

- \frac{3}{2}

and less than or equal to

3

Option C (Greater than or equal to

- \frac{3}{2}

and less than or equal to

3

) is correct because the expression can be rewritten as a quadratic in

\cos \theta

, and its range can be determined.

Practice All Chapter MCQs →

1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ = \lambda \cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin \,\,33^\circ

\lambda =

\cos \,\,\frac{\pi }{{11}} + \cos \,\,\frac{{3\,\pi }}{{11}} + \cos \,\,\frac{{5\,\pi }}{{11}} + \cos \,\,\frac{{7\pi }}{{11}} + \cos \,\,\frac{{9\,\pi }}{{11}}

\;\cos \,\,x + \cos \,\,y + \cos \,\,\alpha = 0\;\,\mathrm{and}\,\sin x + \sin \,\,y + \sin \,\,\alpha = 0

\cot \left( {\frac{{x + y}}{2}} \right)\;

f\left( x \right) = \sin \left( {\frac{{2x + 3}}{{6\;\pi }}} \right),

0 < x,\mathrm{ }y < \pi

\cos x + \cos y - \cos (x + y) = \frac{3}{2}

\sin x + \cos y

\mathrm{\;sin}\,\,36^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,108^\circ \,\,\sin \,\,144^\circ \;