For the expression $(\alpha \tan \gamma +\beta \cot \gamma )(\alpha \cot \gamma +\beta \tan \gamma )-4\alpha \beta {\cot }^{2}2\gamma$ which of the following is/are true?

Important Questions on Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 1

The value of $4\cos 18°-\frac{3}{\cos 18°}-2\tan 18°$ is equal to:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 2

The value of $\frac{\cot 84°\cot 48°}{\cot 66°\cot 78°}$ is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 3

If $\tan \frac{\pi }{24}=(\sqrt{p}-\sqrt{q})(\sqrt{r}-s)$ then the value of  $(p+q+r+s)$, where $p, q, r \& s$ are least positive integers, is:

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 4

In a $∆ABC,$$2 \sin A\cos B+2\sin B\cos C+2 \sin C\cos A=\sin A+\sin B+\sin C$, then $∆ABC$ is: 

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 5

If $\cos A$, $\cos B$ and $\cos C$ are the roots of the value cubic $x^3+a{x}^2+bx+c=0$, where $A,B,C$ are the angles of a triangle then the value $a^2-2b-2c$ is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 6

If $A+B+C+D=2\pi$, then $\cos A+\cos B+\cos C+\cos D=$

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 7

If $A,B,C,D$ are the angles of a quadrilateral, then $\frac{\tan A+\tan B+\tan C+\tan D}{\cot A+\cot B+\cot C+\cot D}=$

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 3 - Trigonometric Ratios for Compound, Multiple, Sub-multiple Angles, and Transformation Formulas>DPP>Q 8

The value of ${\cos }^2\frac{\pi }{11}+{\cos }^2\frac{2\pi }{11}+{\cos }^2\frac{3\pi }{11}+{\cos }^2\frac{4\pi }{11}+{\cos }^2\frac{5\pi }{11}$is: