$\,\,5.\,\,$ If $\,\sin\theta=\frac 35,\,\,\tan\phi=\frac{8}{15}\,\,$ and $\,\theta\,\,$ and $\,\,\phi\,$ lie in the fi…

$\,3(i).\,$ If $\,\,\alpha,\,\,\beta\,\,$ are positive acute angles and $\,\,(a)\,\,\sin\alpha=\frac{1}{\sqrt5},\,\,\…

$\,1.\,$  Find the values : $\,(i)\,\,\sin(-75^{\circ})\\=-\sin 75^{\circ}\\=-\sin(30^{\circ}+45^{\circ})\\=-[\sin 30…

$\,10(i).\,$ If $\,\,\cot\alpha\cot\beta=3,\,\,$ show that , $\,\,\frac{\cos(\alpha-\beta)}{\cos(\alpha+\beta)}=2.$ S…

$\,3.\,$ Find the expansions : $\,(i)\,\,\,\sin(A-B+C)$ Sol. $\,\,\,\sin(A-B+C)\\=\sin[(A-B)+C]\\=\sin(A-B)\cos C+\c…

$\,1(i).\,$ Prove that, $ \,\,\,\sin^2\alpha+\sin^2(120^{\circ}-\alpha)+\sin^2(120^{\circ}+\alpha)\\=\frac 32.$ Sol. …

$\,6.\,$ If $\,\,\sin\theta=k\sin(\theta+\phi),\,\,$ show that, $\,\,\tan(\theta+\phi)=\frac{\sin\phi}{\cos\phi-k}.$ …

$\,1.\,$ Prove that, $\,\,\tan(A+B)-\tan(A-B)=\frac{\sin 2B}{\cos^2B-\sin^2A}.$ Sol.  We have, $\,\,\tan(A+B)-\tan(A-…