Trigonometric Ratios & Identities · Mathematics · TS EAMCET

If $(\sin \theta-\operatorname{cosec} \theta)^{2}+(\cos \theta+\sec \theta)^{2}=5$ and $\theta$ lies in the third quadrant, then $(\sin \theta+\cos \theta)^{3}=$

If $0 < B < A < \frac{\pi}{4}, \cos ^{2} B-\sin ^{2} A=\frac{\sqrt{3}+1}{4 \sqrt{2}}$ and $2 \cos A \cos B=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\cos ^{2} \frac{4 B}{3}-\sin ^{2} \frac{4 A}{5}=$

If $\theta$ is an acute angle and $2 \sin ^{2} \theta=\cos ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\cos ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{7 \pi}{8}$, then $\theta=$

If $2 \tan ^{2} \theta-4 \sec \theta+3=0$, then $2 \sec \theta=$

If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta+15 \sin \theta=15$, then $15 \cos \theta-8 \sin \theta=$

$\sin 20^{\circ}\left(4+\sec 20^{\circ}\right)=$

If $\sin h x=\frac{12}{5}$, then $\sin h 3 x+\cos h 3 x=$

$\tan A=\frac{-60}{11}$ and $A$ does not lie in the 4th quadrant. $\sec B=\frac{41}{9}$ and $B$ does not lie in the 1st quadrant. If $\operatorname{cosec} A+\cot B=K$, then $24 K=$

If $\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K$ and $\cot A+\tan A=2 K$, then the possible values of $\tan A$ are

The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ}$ $=0.0174$ and $\sqrt{3}=1.732$ is

The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is

If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$

If $\tan A<0$ and $\tan 2 A=-\frac{4}{3}$, then $\cos 6 A=$

If $m \cos (\alpha+\beta)-n \cos (\alpha-\beta)$ $=m \cos (\alpha-\beta)+n \cos (\alpha+\beta)$, then $\tan \alpha \tan \beta=$