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The value of the expression $$[\text{cosec(}75^{\small\circ}+\theta) - \sec(15^{\small\circ}- \theta) - \tan(55^{\small\circ} + \theta) + \cot(35^{\small\circ} - \theta)]$$ is

If $$\sin\theta = \displaystyle\frac{12}{13}$$, then the value of $$\displaystyle\frac{2\cos\theta + 3\tan\theta}{\sin\theta + \tan\theta\sin\theta}$$

If $$\sec{\theta}+\tan{\theta}=P$$, then the value of $$\sin{\theta}$$ is

If $$ \sin{x}+\sin^{2}{x}=1$$, then the value of $$\cos^{2}{ x}+\cos^{4}{x}$$ is 

If $$tan\theta=\sqrt {\displaystyle \frac {a}{b}}$$ where $$a, b$$ are positive reals, then the value of $$\sin\theta \sec^7\theta+\cos\theta co\sec^7\theta$$ is

If $$\sin\theta+co\sec\theta=2$$, then the value of $$\sin^8\theta+co\sec^8\theta$$ is equal to

If $$\tan A = \displaystyle\dfrac{3}{4}$$ and $$A+B = 90^{\small\circ}$$, then what is the value of $$\cot B$$?

If $$(x-2)\sin^230^{\small\circ} + (x-3)\tan^260^{\small\circ} - x\cos^245^{\small\circ} = \displaystyle\frac{17}{4}$$, find the value of $$x$$.

$$\sqrt{(1-\cos^2\theta)\sec^2\theta} = \tan\theta$$.Is it true or false?

If $$\sin \theta + \cos \theta = 1$$, then $$\sin \theta \cos \theta =$$.