What are the most general values of $\theta$ which satisfy the following equation: $2{\cot }^2\theta ={\mathrm{cosec}}^2\theta$?

Important Questions on General Expressions for All Angles Having a Given Trigonometrical Ratio

MEDIUM

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 17

What are the most general values of $\theta$ which satisfy the following equation: ${\sec }^2\theta =\frac{4}{3}$?

MEDIUM

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 18

What is the most general value of $\theta$ that satisfies both of the equations $\cos \theta =-\frac{1}{\sqrt{2}} \& \tan \theta =1$?

EASY

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 19

What is the most general value of $\theta$ that satisfies both of the equations: $\cot \theta =-\sqrt{3} \& \mathrm{cosec}\theta =-2$?

MEDIUM

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 20

If $\cos (A-B)=\frac{1}{2}$ and $\sin (A+B)=\frac{1}{2},$ find the smallest positive values of $A$ and $B$ and also their most general values. 

MEDIUM

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 21

If $\tan (A-B)=1$ and $\sec \left(A+B\right)=\frac{2}{\sqrt{3}},$ find the smallest positive values of $A$ and $B$ and also their most general values. 

EASY

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 22

Find the angles between $0^{\mathrm{o}}$ and ${360}^{\mathrm{o}}$ which have their sines equal to $\frac{\sqrt{3}}{2}$.

EASY

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 22

Find the angles between $0^{°}$ and ${360}^{°}$ which have their cosines equal to $-\frac{1}{2}$.

EASY

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 6 - General Expressions for All Angles Having a Given Trigonometrical Ratio>EXAMPLES XI>Q 22

Find the angles between $0^{°}$ and ${360}^{°}$ which have their tangents equal to $\frac{1}{\sqrt{3}}$.