What is the maximum value of ${\sin }^{2}x ?$

Important Questions on Measurement of Angles and Trigonometric Ratios

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 33

If $\cot A·\cot B=2,$ then what is the value of $\cos \left(A+B\right)·\sec \left(A-B\right)?$

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 34

What is the maximum value of $\sin 3\theta \cos 2\theta +\cos 3\theta \sin 2\theta ?$

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 35

What is the value of ${\sec }^2\left\{{\tan }^{-1}\left(\frac{5}{11}\right)\right\}?$

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 36

What is the value of $\sin A\cos A\tan A+\cos A\sin A\cot A?$

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 37

If $\tan \theta +\sec \theta =4,$ then what is the value of $\sin \theta ?$

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 38

What is the value of $\sin 420°·\cos 390°+\cos \left(-300°\right)·\sin \left(-330°\right) ?$

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 39

If $\theta =18°,$ then what is the value of $4{\sin }^2\theta +2\sin \theta ?$

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 15 - Measurement of Angles and Trigonometric Ratios>Practice Exercise>Q 40

What is the value of $\tan \left(\frac{\pi }{12}\right)?$