Trigonometry MCQs

The value of $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ } + 4{\text{se}}{{\text{c}}^2}{{30}^ \circ } - {\text{ta}}{{\text{n}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{30}^ \circ } + {\text{co}}{{\text{s}}^2}{{30}^ \circ }}}$$      is?

If θ is positive acute angle and 3(sec²θ + tan²θ) = 5, then the value of cos2θ is?

$$\frac{{\left( {2\sin A} \right)\left( {1 + \sin A} \right)}}{{1 + \sin A + \cos A}}$$    is equal to:

Find the value of the following 3(sin⁴θ + cos⁴θ) + 2(sin⁶θ + cos⁶θ) + 12sin²θ.cos²θ = ?

The value of 152(sin30° + 2cos²45° + 3sin30° + 4cos²45° + ...... + 17sin30° + 18cos²45°) is?

If $$2\sin \left( {\frac{{\pi x}}{2}} \right) = {x^2} + \frac{1}{{{x^2}}}{\text{,}}$$     then the value of $$\left( {x - \frac{1}{x}} \right)$$   is?

What is the value of $$\frac{{1 + 2{{\cot }^2}\left( {{{90}^ \circ } - x} \right) - 2{\text{cosec}}\left( {{{90}^ \circ } - x} \right)\cot \left( {{{90}^ \circ } - x} \right)}}{{{\text{cosec}}\left( {{{90}^ \circ } - x} \right) - \cot \left( {{{90}^ \circ } - x} \right)}}?$$

If A = tan11°. tan29°, B = 2cot61°. cot79° then -

$$\frac{{{{\left( {1 + \sec \theta \,{\text{cosec}}\,\theta } \right)}^2}{{\left( {\sec \theta - \tan \theta } \right)}^2}\left( {1 + \sin \theta } \right)}}{{{{\left( {\sin \theta + \sec \theta } \right)}^2} + {{\left( {\cos \theta + {\text{cosec}}\,\theta } \right)}^2}}},$$        0° < θ < 90°, is equal to: