Trigonometry MCQs

If $${\text{sin}}\left( {{{60}^ \circ } - \theta } \right)$$   = $${\text{cos}}\left( {\psi - {{30}^ \circ }} \right),$$   then the value of $${\text{tan}}\left( {\psi - \theta } \right)$$   is (assume that $$\theta $$ and $$\psi $$ are both positive acute angles with$$\theta < {60^ \circ }$$ and $$\psi > {30^ \circ }$$  ) ?

Evaluate the following expression in terms of trigonometric ratios. $$\frac{{\sec A - \tan A}}{{\sec A + \tan A}}$$

If $$\frac{{{{\sec }^2}{{70}^ \circ } - {\text{co}}{{\text{t}}^2}{{20}^ \circ }}}{{2\left( {{\text{cose}}{{\text{c}}^2}{{59}^ \circ } - {{\tan }^2}{{31}^ \circ }} \right)}}$$     = $$\frac{2}{m}{\text{,}}$$  then m is equal to?

If a right-angled triangle XYZ right-angled at Y. If XY = $${\text{2}}\sqrt 6 $$  and XZ - YZ = 2, then secX + tanX is?

The simplified value of (secA - cosA)² + (cosecA - sinA)² - (cotA - tanA)²

If cos²θ - sin²θ = $$\frac{1}{3}{\text{,}}$$ where 0 ≤ θ ≤ $$\frac{\pi }{2}{\text{,}}$$ then the value of cos⁴θ - sin⁴θ is?

Which one of the following is true for 0° < θ < 90° ?

If sinθ = $$\frac{a}{b}$$  then the value of secθ - cosθ is? (where 0° < θ < 90°)

If $${\text{sin A}} - \cos {\text{A}}$$   = $$\frac{{\sqrt 3 - 1}}{2}{\text{,}}$$   then the value of $${\text{sin A}}.{\text{cosA}}$$   is?