If $x=\sec \varphi -\tan \varphi$ and $y=cosec\varphi +\cot \varphi ,$ then

Important Questions on Trigonometric Functions and Identities

HARD

JEE Main

IMPORTANT

Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 39

In an isosceles right-angled triangle, a straight line drawn from the midpoint of one of the equal sides to the opposite angle. It divides the angle into two parts, $\theta$ and $\left(\frac{\pi }{4}-\theta \right).$ Then tan $\theta$ and $\tan \left(\frac{\pi }{4}-\theta \right)$ are equal to
 

HARD

JEE Main

IMPORTANT

Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 40

If $3{\sin }^{2}A+2{\sin }^{2}B=1$ and $3\sin 2A-2\sin 2B=0,$ where $A$ and $B$ are acute angles, then $\left(A+2B\right)$ is equal to