Trigonometric Equations

Maximum value of $(2\sin \theta +3\cos \theta )$ is _____.

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

If $\mathrm{tanA}=\frac{1-\mathrm{cosB}}{\mathrm{sinB}}$, then what is$\frac{2\mathrm{tanA}}{1-{\tan }^2\mathrm{A}}$  equal to ______.

If $\sin (3\mathrm{\alpha }-\mathrm{\beta })=1$ and $\cos (2\mathrm{\alpha }+\mathrm{\beta })=\frac{1}{2}$, then the value of$\tan \mathrm{\alpha }$is ______.

If $8\sin x=4+\cos x$, the values of $\sin x$ are:

If $\sin \mathrm{x}+{\sin }^2\mathrm{x}+{\sin }^3\mathrm{x}=1,$ then${\cos }^6\mathrm{x}-4 {\cos }^4\mathrm{x}+8 {\cos }^2\mathrm{x}$ is equal to _____.

The value of $\sin i$ and $\cos i$ is always less than $1$ in $0<i<90°$. Then the value of $\sin i+\cos i$ is _____.

If $\sin \mathrm{\theta }+\cos \mathrm{\theta }=\mathrm{p}$ and $\sec \mathrm{\theta }+\mathrm{cosec} \mathrm{\theta }=\mathrm{q}$, then the value of $\mathrm{q}({\mathrm{p}}^2-1)$ is _____.

If $\sin 17°=\frac{\mathrm{x}}{\mathrm{y}}$, then the value of $\sec 17°-\sin 73°$ is _____.

If $3\sin \mathrm{x}+5\cos \mathrm{x}=5$, then what is the value of $(3\cos \mathrm{x}-5\sin \mathrm{x})$ ______.

The value of $\frac{{cos}^3\theta +{sin}^3\theta }{cos\theta +sin\theta }+\frac{{cos}^3-{sin}^3\theta }{cos\theta -sin\theta }$ is equal to_____

The value of $\sin {10}^{°} \sin {30}^{°} \sin {50}^{°} \sin {70}^{°}$ is  _______.

$\cos 2\theta + 2\cos \theta$ is always-

If $\cos \left(\alpha +\beta \right)=\frac{4}{5}$ and $\sin \left(\alpha -\beta \right)=\frac{5}{13}$, where $\alpha , \beta$ lies between $0 \& \frac{\pi }{4}$, then the value of $\tan 2\alpha$ is __________.

If $7{\sin }^2\mathrm{a}+3{\cos }^2\mathrm{a}=4$ and $0<\mathrm{a}<\frac{\mathrm{\pi }}{2}$, then the value of $\tan \mathrm{a}$ is ______.

The value of $4{\cot }^{2}45°–{\sec }^{2}60°+{\sin }^{2}30°$ is ____.

If $\mathrm{sin\alpha }.\mathrm{sin\beta }—\mathrm{cos\alpha }.\mathrm{cos\beta }+1=0$,then the value of $1+\mathrm{cot\alpha }.\mathrm{tan\beta }$ is_____.

If $\tan \mathrm{\theta }+\sin \mathrm{\theta }=\mathrm{m}$ and $\tan \mathrm{\theta }–\sin \mathrm{\theta }=\mathrm{n}$, then ${\mathrm{m}}^2–{\mathrm{n}}^2$ is equal to -

If $\tan A=\sqrt{2}-1$ then value of $\sin 2A$ is _______.

$\sin \frac{\mathrm{\pi }}{6}+\cos \frac{\mathrm{\pi }}{3}{\tan }^3\frac{\mathrm{\pi }}{4}+se{c}^2\frac{\mathrm{\pi }}{2}=?$