My niece believes everything she hears.  

If cot5A = tan(3A-14˚), find the value of A? Given that 5A and 3A-14˚ are acute angles.

If tan 3.5θ x tan 6.5θ = 1 then the value of tan 5θ is

If cos² x + sin x = 5/4, then find the value of 'sin x'.

If A and B are complementary angles, then the value of-

sin A cos B + cos A sin B – tan A tan B + sec ²

If cot2A = tan(A+6˚ )  , find the value of A? Given that 2A and A+6˚  are acute angles.

sin² 7˚ + sin² 9˚ + sin² 11˚ + sin² 12˚ + ……… + sin² 83˚ = ?

If sin x + cos x = √2 sin x, then the value of sin x - cos x is:

Simplify: sin 780° sin 480° + cos 120° sin 30°