Introduction to...

If $$\displaystyle \frac{\sin x}{a}= \frac{\cos x}{b}= \frac{\tan x}{c}= k,$$ then $$\displaystyle bc+\frac{1}{ck}+\frac{ak}{1+bk} $$ is equal to

If $$\displaystyle \sin \theta+\sin ^{2} \theta +\sin ^{3}\theta= 1$$ then the value of $$\displaystyle \cos ^{6}\theta-4\cos ^{4}\theta+8\cos ^{2}\theta$$ equals

If $$\displaystyle \sin x+ \sin^{2}x= 1,$$ then the value of $$\displaystyle \cos ^{12}x +3\cos ^{10}x+3\cos ^{8}x+\cos ^{6}x-2$$ is equal to

Use the information given to find the length of $$AB$$ in cm

If $$\displaystyle \cos A= \frac{1}{2}$$ and $$\displaystyle \sin B= \frac{1}{\sqrt{2}}$$ , find the value of $$\displaystyle \frac{\tan A\, -\, \tan B}{1\, +\, \tan A\tan B}$$

If $$\displaystyle \frac{\cos ^{4}\theta} {\theta_{1}}+\frac{\sin ^{4}\theta} {\theta_{2}}= \frac{1}{\theta_{1}+\theta_{2}}$$ ,then $$\displaystyle \frac{\theta_{2}+\theta_{1}}{\theta_{1}}$$ equals

The value of the expression $$\displaystyle \frac{\cos ^{2}\alpha \sin ^{2}\theta +\sin ^{2}\alpha }{\tan ^{2}\theta+\sin ^{2}\alpha }$$ equals 

If $$\displaystyle\frac{\cos^{4}x }{\theta _{1}}+\displaystyle\frac{\sin^{4}x}{\theta _{2}}=\frac{1}{\theta _{1}+\theta _{2}},$$ then $$\displaystyle\frac{\theta _{2}}{\theta _{1}}$$ equals

$$\cfrac { \cos { \theta  }  }{ 1-\sin { \theta  }  } -\cfrac { \cos { \theta  }  }{ 1+\sin { \theta  }  } =2$$ is satisfied by which one of the following values of $$\theta$$?

Evaluate :$$\displaystyle \frac{5\cos ^{2}60^{\circ}+4\sec ^{2}30^{\circ}-\tan ^{2}45^{\circ}}{\sin ^{2}30^{\circ}+\cos ^{2}30^{\circ}}$$