Trigonometric Ratios & Identities - Trigonometry PYQs

In a \(\triangle A B C\), if \(3 \sin A+4 \cos B=6\) and \(4 \sin B+3 \cos A=1\), then \(\sin (A+B)\) is equal to

\(\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha\) is equal to

Mean of the values \(\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y\) is

In \(\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3\), then \(\tan \frac{C}{8}\) is equal to

If \(f(x)=\frac{\cot x}{1+\cot x}\) and \(\alpha+\beta=\frac{5 \pi}{4}\), then the value of \(f(\alpha) f(\beta)\) is equal to

When the coordinate axes are rotated through an angle 135\(\Upsilon\), the coordinates of a point \(P\) in the new system are known to be \((4,-3)\). Then find the coordinates of \(P\) in the original system.

The maximum value of \(f(x)=\sin (x)\) in the interval \(\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]\) is

If \(\sin \alpha - \cos \alpha = m\) and \(\sin 2\alpha = n - {m^2}\), where \(- \sqrt 2 \le m \le \sqrt 2\), then n is equal to

If \(\sinh u=\tan \theta\), then \(\cosh u\) is equal to

\(\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)\) is equal to

If \(A+B+C=\frac{3 \pi}{2}\), then \(\cos 2 A+\cos 2 B+\cos 2 C\) is equal to

Let \(\theta\) be an angle in the standard position such that the point \((-5,12)\) lies on its terminal side, then

If \(\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32}=2^m \operatorname{cosec} \frac{\pi}{n}\), then \(m+n\) is equal to

\(\sinh (x+y) \cosh (x-y)\) is equal to

The sides of a triangle inscribed in a given circle subtend angles \(\alpha, \beta, \gamma\) at the center. The minimum value of the AM of \(\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)\) and \(\cos \left(\gamma+\frac{\pi}{2}\right)\) is equal to

What is the value of \(\cos \left(22 \frac{1}{2}\right)^{\circ}\) ?

If \(\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}\), then \(\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}\) is equal to

If \(\cos \theta=-\sqrt{\frac{3}{2}}\) and \(\sin \alpha=\frac{-3}{5}\), where '\(\theta\)' does not lie in the third quadrant, then the value of \(\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}\) is equal to

A true statement among the following identities is

If \(A+B+C=\pi, \cos B=\cos A \cos C\), then \(\tan A \tan C=\)