Trigonometric F...

If $$ X\sin { \left( { 90 }^{ \circ  }-\theta  \right) \cot { \left( { 90 }^{ \circ  }-\theta  \right)  }  } =\cos { \left( { 9 }0^{ \circ  }-\theta  \right)  } $$, then x =

The value of $$\operatorname { \sec } ^ { 2 } A \operatorname { \tan } ^ { 2 } B - \tan ^ { 2 } A \operatorname { \sec } ^ { 2 } B $$ is

$$\dfrac{\cos(90-A)\sin(90-A)}{\tan (90-A)}$$=

Which of the following is the principal value of $$\cos { ^{ -1 }\left( \dfrac { -1 }{ 2 }  \right)  } $$?

If $$cos x=b$$, then for what b do the roots of the equation form an AP ?

What is the value of $$\cfrac{\tan{A}-\sin{A}}{\sin^3{A}}$$?

The range of the function $$f(x)=\left (\cos ^2x+4\sec ^2x\right )$$ is

The principle solution of equation $$\cot x =  - \sqrt 3 $$ is 

$$\displaystyle 1^c =?$$

Let $$n$$ be a positive integer such that
$$\displaystyle \sin(\frac{\pi}{2^{n}})+\cos(\frac{\pi}{2^{n}})=\frac{\sqrt{n}}{2}$$