Assignment

Find the value of $\sqrt{3}cosec20°-\sec 20°$.

Prove that ${\cos }^{2}A+{\cos }^2\left(A+120°\right)+{\cos }^2\left(A-120°\right)=\frac{3}{2}$

Prove that $\tan 189°=\frac{\cos 36°-\sin 36°}{\cos 36°+\sin 36°}$.

Compare $\sin 1$ and $\sin 2,\cos 1$ and $\cos 2,\tan 1$ and $\tan 2$.

If $A={\cos }^2\theta +{\sin }^4\theta$ for all values of $\theta$, then prove that $\frac{3}{4}\le A\le 1$.

In $∆ABC$ if $\sin A:\sin B:\sin C=1:2:2$, then find the value of $\cos A$.

If $\sin \theta +\cos \theta =m$ and $\sec \theta +\cos ec\theta =n$, then prove that $n\left(m+1\right)\left(m-1\right)=2m$.

Prove that $\sin \alpha +\sin \left(\alpha +\frac{2\pi }{3}\right)+\sin \left(\alpha +\frac{4\pi }{3}\right)=0$.