Trigonometry MCQs

Let A, B, C, D be the angles of a quadrilateral. If they are concyclic, then the value of cos A + cos B + cos C + cos D is ?

If $$\left( {\frac{{\tan \theta - \sec \theta + 1}}{{\tan \theta + \sec \theta - 1}}} \right)\sec \theta = \frac{1}{{\text{k}}},$$      then k = . . . . . . . .

If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is?

What is the value of $$\frac{{3\sin {{58}^ \circ }}}{{\cos {{32}^ \circ }}} + \frac{{3\sin {{42}^ \circ }}}{{\cos {{48}^ \circ }}}$$

The value of $$\frac{{\cot {{30}^ \circ } - \cot {{75}^ \circ }}}{{\tan {{15}^ \circ } - \tan {{60}^ \circ }}}$$    is?

If $$r\sin \theta = 1,$$   $$r\cos \theta = \sqrt 3 ,$$   then the value of $$\left( {\sqrt 3 {\text{tan}}\theta + 1} \right)$$   = ?

The expression $$\frac{{{{\cos }^4}\theta - {{\sin }^4}\theta + 2{{\sin }^2}\theta + 3}}{{\left( {{\text{cosec}}\,\theta + \cot \theta + 1} \right)\left( {{\text{cosec}}\,\theta - \cot \theta + 1} \right) - 2}},$$         is equal to:

The value of $$\frac{{{\text{sin A}}}}{{1 + \cos {\text{ A}}}}$$   + $$\frac{{{\text{sin A}}}}{{1 - \cos {\text{ A}}}}$$   is $$\left( {{0^ \circ } < {\text{A}} < {{90}^ \circ }} \right)$$

The value of the following is : $${\left( {\frac{{{\text{sin 4}}{{\text{7}}^ \circ }}}{{\cos {{43}^ \circ }}}} \right)^2}$$   + $${\left( {\frac{{\cos {{43}^ \circ }}}{{{\text{sin }}{{47}^ \circ }}}} \right)^2}$$   - $$4{\text{co}}{{\text{s}}^2}{45^ \circ }$$   = ?