If $\sin 2\theta +\sin 2\varphi =\frac{1}{2}$ and $\cos 2\theta +\cos 2\varphi =\frac{3}{2}$, then ${\cos }^2(\theta -\varphi )=$

Important Questions on Trigonometric Functions of Compound Angles

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 68

If $n=1, 2, 3,\dots$, then $\cos \alpha \cos 2\alpha \cos 2^2\alpha \cos 2^3\alpha \dots \cos 2^{n-1}\alpha$ is equal to

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 69

$\cos \frac{2\pi }{15} \cos \frac{4\pi }{15} \cos \frac{8\pi }{15} \cos \frac{16\pi }{15}=$

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 70

If $k=\sin \frac{\pi }{18}\sin \frac{5\pi }{18}\sin \frac{7\pi }{18}$, then the numerical value of $k$ is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 71

The value of $\sin \left(\frac{\pi }{14}\right) \sin \left(\frac{3\pi }{14}\right) \sin \left(\frac{5\pi }{14}\right) \sin \left(\frac{7\pi }{14}\right) \sin \left(\frac{9\pi }{14}\right) \sin \left(\frac{11\pi }{14}\right) \sin \left(\frac{13\pi }{14}\right)$ is equal to

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 72

The value of $\sin \frac{31}{3}\pi$ is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 73

The value of $\tan \frac{\pi }{5}+2\tan \frac{2\pi }{5}+4\cot \frac{4\pi }{5}$ is

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 74

The value of $\frac{\cot x-\tan x}{\cot 2x}$ is

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Trigonometric Functions of Compound Angles>Competitive Thinking>Q 75

$\frac{\sec 8A-1}{\sec 4A-1}=$