1. The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is

2. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

3. The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is

4.  If cosT = 3/5 and if sin R = 8/17 , where T is in the fourth quadrant and R is in the second quadrant, then cos (T – R) is equal to:   

5. The value of cos 20 + 2sin² 55 – √2 sin65 is

6. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is

7.  If tan q = -4/3 , then sin q is 

8. If sin q and cos q are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation. 

9. The value of cos² x + cos² y – 2cos x × cos y × cos (x + y) is

10. If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is

11. What is the value of (secq – cosq) ( cotq + tanq ) ?

12. If cos a + 2cos b + cos c = 2 then a, b, c are in

13. If 3 × tan(x – 15) = tan(x + 15), then the value of x is

14. The value of cos 5π is

15. If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is

16. The value of tan 20 × tan 40 × tan 80 is

17. The general solution of √3 cos x – sin x = 1 is

18. The value of cos 180° is

19. If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

20. The general solutions of the following equation : tan 2q = 0 is