List of top Mathematics Questions on Trigonometric Ratios of Some Specific Angles

The value of \(2\tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ\) is \dots
State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin \(\text{θ}\) increases as \(\text{θ}\) increases.
(iii) The value of cos \(\text{θ}\) increases as \(\text{θ}\) increases.
(iv) sin \(\text{θ}\) = cos \(\text{θ}\) for all values of \(\text{θ}\).
(v) cot A is not defined for A = 0°
If tan (A + B) = \(\sqrt3\) and tan (A - B) = \(\frac{1}{\sqrt3}\); 0°\( <\) (A + B) \(≤\) 90° ; A > B, find A and B
Choose the correct option and justify your choice: \(\frac{2\ tan\ 30°}{1 - tan^2 30°} =\)
Choose the correct option and justify your choice: sin 2A = 2 sin A is true when A =
Choose the correct option and justify your choice: \(\frac{1 - tan^2 45°}{1 + tan^2 45°} =\)
Choose the correct option and justify your choice: \(\frac{2\ tan\  30°}{1 + tan^2 30°} =\)

Evaluate the following. 
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan245° + cos230° - sin260°
(iii) \(\frac{cos 45°}{sec 30°+cosec30°}\)


(iv) \(\frac{sin\ 30°+tan\ 45°cosec\ 60°}{sec\ 30°+cos\ 60°+cot\ 45°}\)


(v) \(\frac{5cos^260°+4sec^230°-tan^245°}{sin^230°+cos^230°}\)