Trigonometry MCQs

The value of $$\frac{{\sin A}}{{\cot A + {\text{cosec}}\,A}} - \frac{{\sin A}}{{\cot A - {\text{cosec}}\,A}} - 1{\text{ is:}}$$

Simplify: cos(36° - A)cos(36° + A) + cos(54° - A)cos(54° + A)

What is the value of $$\sin \left( {180 - \theta } \right)\sin \left( {90 - \theta } \right) + \frac{{\cot \left( {90 - \theta } \right)}}{{1 + {{\tan }^2}\theta }}?$$

The value of $$\frac{{3\left( {{\text{cose}}{{\text{c}}^2}{{26}^ \circ } - {{\tan }^2}{{64}^ \circ }} \right) + \left( {{{\cot }^2}{{42}^ \circ } - {{\sec }^2}{{48}^ \circ }} \right)}}{{\cot \left( {{{22}^ \circ } - \theta } \right) - {\text{cose}}{{\text{c}}^2}\left( {{{62}^ \circ } + \theta } \right) - \tan \left( {\theta + {{68}^ \circ }} \right) + {{\tan }^2}\left( {{{28}^ \circ } - \theta } \right)}}\,{\text{is:}}$$

The value of 8(sin⁶θ + cos⁶θ) - 12(sin⁴θ + cos⁴θ) is equal to?

If $$\frac{{\sec \theta - \tan \theta }}{{\sec \theta + \tan \theta }} = \frac{1}{7},\,\theta ,$$     lies in first quadrant, then the value of $$\frac{{{\text{cosec}}\,\theta + {{\cot }^2}\theta }}{{{\text{cosec}}\,\theta - {{\cot }^2}\theta }}$$   is:

The value of, $${\text{sec}}\theta \left( {\frac{{1 + \sin \theta }}{{{\text{cos}}\theta }} + \frac{{{\text{cos}}\theta }}{{1 + \sin \theta }}} \right)$$      - $$2{\text{ta}}{{\text{n}}^2}\theta $$   is?

If sinP + cosecP = 2, then the value of sin⁷P + cosec⁷P is?

The value of cot 18° $$\left( {{\text{cot 7}}{{\text{2}}^ \circ }{\text{.co}}{{\text{s}}^2}{{22}^ \circ } + \frac{1}{{{\text{tan 7}}{{\text{2}}^ \circ }.{\text{se}}{{\text{c}}^2}{{68}^ \circ }}}} \right)$$      is?