If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1]?

If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ?

What is the value of sin (–π/3) + cos(–π/6)?

If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?

If an equilateral triangle has side 12 cm, then what is the difference (in cm) between the circumradius and inradius?

The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length (in cm) of PQ?

If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

If x – 3 + [1/(x – 3)] = 4, what is the value of [(x – 3)3+ [1/(x – 3)3]?