If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

What is the simplified value of (cos A + sin A)(cot A + tan A)?

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

Circum center of ΔABC is O. If ∡BAC = 75 and ∡BCA = 80 degrees,

then what is the value of ∡OAC(in deg)?

In ΔABC, AD is the median and AD = (1/2)BC. If ∠ACD = 40°, then what is the value (in degrees) of ∠DAB?

If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2?

If (x/y)a-4 = (y/x)2a-5, then what is the relation between x and y?

A train travels 20% faster than a car. Both start from point A at the same time and reach point B, 180 km away at the same time. On the way the train takes 30 minutes for stopping at the stations. What is the speed (in km/hr) of the train?