Trigonometry MCQs

If $$\frac{{\cos \left( {x + A} \right)}}{a} = \frac{{\cos \left( {x + 2A} \right)}}{b} = \frac{{\cos \left( {x + 3A} \right)}}{c}$$        and A = 60°, x = 15°, then the value of $${\left( {\frac{{a + c}}{b}} \right)^2} + {\left( {\frac{{a - c}}{b}} \right)^2}$$   is . . . . . . . .

If a² sec²x - b² tan²x = c², then the value of sec²x + tan²x is equal to (assume b² ≠ a²)

If 3sec²θ + tanθ - 7 = 0, 0° < θ < 90°, then what is the value of $$\left( {\frac{{2\sin \theta + 3\cos \theta }}{{{\text{cosec}}\,\theta + \sec \theta }}} \right)?$$

If cosx + cos²x = 1,the numerical value of (sin¹² + 3sin¹⁰x + 3sin⁸x + sin⁶x - 1) = ?

The value of $$\frac{{{{\sec }^2}\theta }}{{{\text{cose}}{{\text{c}}^2}\theta }} + \frac{{{\text{cose}}{{\text{c}}^2}\theta }}{{{{\sec }^2}\theta }} - \left( {{{\sec }^2}\theta + {\text{cose}}{{\text{c}}^2}\theta } \right){\text{is:}}$$

The numerical value of $$\frac{1}{{1 + {{\cot }^2}\theta }}$$   + $$\frac{3}{{1 + {\text{ta}}{{\text{n}}^2}\theta }}$$   + $$2{\sin ^2}\theta $$   will be?

The expression $$\frac{{{{\left( {1 - \sin \theta + \cos \theta } \right)}^2}\left( {1 - \cos \theta } \right){{\sec }^3}\theta \,{\text{cose}}{{\text{c}}^2}\theta }}{{\left( {\sec \theta - \tan \theta } \right)\left( {\tan \theta + \cot \theta } \right)}},$$        0° < θ < 90°, is equal to:

If secα + tanα = 2, then the value of sinα is (assume that 0 < α < 90°)

If secA + tanA = a, then the value of cosA is?