If $A+B=90°,$ then what is the value of $\sqrt{\sin A\sec B-\sin A\cos B} ?$

Important Questions on Trigonometric Ratios and Identities

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 15

If ${\tan }^2\theta =2{\tan }^2\varphi +1$, then $\cos 2\theta +{\sin }^2\varphi$ equals

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 16

Let $\alpha$ and $\beta$ be such that $\pi <\alpha -\beta <3\pi$, if $\sin \alpha +\sin \beta =-\frac{21}{65}$ and $\cos \alpha +\cos \beta =-\frac{27}{65}$, then the value of $\cos \frac{\alpha -\beta }{2}$ is

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 17

Given that $(1+\sqrt{1+x})\tan y=1+\sqrt{1-x}$, then $\sin 4y$ is equal to

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 18

If an angle $\alpha$ is divided into two parts $A$ and $B$ such that $A-B=x$ and $\tan A: \tan B=2: 1,$ then what is $\sin x$ equal to$?$

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 19

The smallest positive value of $x$ (in degrees) for which $\tan \left(x+100°\right)=\tan \left(x+50°\right)\tan x$ $\tan \left(x-50°\right)$ is

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 20

If $\sin A=\frac{2}{\sqrt{5}}$ and $\cos B=\frac{1}{\sqrt{10}},$ where $A$ and $B$ are acute angles, then what is the value of $A+B?$

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 21

If $A=\left(\cos 12°-\cos 36°\right)\left(\sin 96°+\sin 24°\right)$ and $B=\left(\sin 60°-\sin 12°\right)\left(\cos 48°-\cos 72°\right),$ then what is $\frac{A}{B}$ equal to ? 

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 5 - Trigonometric Ratios and Identities>Exercise 1>Q 22

If $\tan \beta =\cos \theta \tan \alpha$, then ${\tan }^2\frac{\theta }{2}$ equals to