Trigonometric Ratios of Allied Angles

If $\theta$ is acute and $\sin \theta =\cos 2\theta$, then $(\sin \theta +\cos \theta )=?$

Find the value of $\sec \left(315°\right)$.

Find the value of $\cos \left(315°\right)$.

Find the value of $\sin \left(315°\right)$.

Find the value of $\cot \left(315°\right)$.

Find the value of $\tan \left(315°\right)$.

If matrix $A=F\left(\alpha \right)=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0\\ \sin \alpha & \cos \alpha & 0\\ 0& 0& 1\end{array}\right]$, then find $A^{-1}$ and prove that: $A^{-1}=F(-\alpha )$.

Find the value to the following trigonometric function:

$\cot \left(\frac{-15\pi }{4}\right)$

Find the value to the following trigonometric function:

$cosec\left(-1410°\right)$

Find the value of the expression ${\cos }^4\frac{\pi }{8}+{\cos }^4\frac{3\pi }{8}+{\cos }^4\frac{5\pi }{8}+{\cos }^4\frac{7\pi }{8}$

Find the value of the expression $3\left[{\sin }^4\left(\frac{3\pi }{2}-\alpha \right)+{\sin }^4(3\pi +\alpha )\right]-2\left({\sin }^6\left(\frac{\pi }{2}+\alpha \right)+{\sin }^6(5\pi -\alpha )\right]$.

Value of $\cos A-\sin A$, at $A=\frac{5\pi }{4}$ is

If $P, Q$ and $R$ are interior angles of$∆PQR$ , then the value of $\csc \left(\frac{Q}{2}\right)$ is equal to:

The value of $3\left[{\sin }^4\left(\frac{3\pi }{2}-\alpha \right)+{\sin }^4(3\pi +\alpha )\right]-2\left[{\sin }^6\left(\frac{\pi }{2}+\alpha \right)+{\sin }^6(5\pi -\alpha )\right]$is equal to

The value of ${\cos }^2\left(\frac{\mathrm{\pi }}{4}+\theta \right)-{\sin }^2\left(\frac{\mathrm{\pi }}{4}-\theta \right)$ is

The value of $\mathrm{tan }1°\mathrm{ tan }2°\mathrm{ tan }3°\dots \mathrm{tan }89°$ is equal to