Answer the following:

1. Find the value of
2. Evaluate cos 15^o –sin 15^o
3. If where α and β are acute angles, show that
4. The circular measures of two angles of a triangle are ½ and 1/3 , find the third angle in English system [ ans : 132^o 16’ 22’’ ]
5. A circular wire of radius 3 cm is cut and bent so as to lie along a circle of radius 48cm. Find the angle subtended by the wire at the centre of the circle [ans : 22.5^o]
6. Find the angle between the hands of a clock at 7:20 P.M. [ ans: 100^o]
7. If
8. If sec x + tan x = 4 , find sin x and cos x. Also find the quadrant in which x lies.

[ ans : sin x = 15/17 , cos x == 8/17 , First ]

1. If

1. If tan A + cot A = 2, then find tan¹⁰⁰A + cot¹⁰⁰A [ans : 2 ]
2. Prove that
3. Prove that tan tan tan tan tan = 1
4. Prove that cos +cos +cos =
5. Prove that sin 10 ^o sin 50^o sin 70 ^o =
6. Prove that cos10^o cos 30^o cos 50^o cos 70 ^o =
7. Prove that + + = 0
8. If cosx +cosy = and sinx+siny = tan
9. Prove that
10. Prove that = tanx
11. Prove that cos 5x = 16cos ⁵ x -20 cos ³ x +5cosx
12. Solve the equation cosx + sin x = cos2x + sin2x
13. Find all values of A between 0^o and 720^o which satisfy the equation

2 cos²A -5cosA + 2 = 0 [ans : 60 ^o, 300 ^o, 420 ^o, 660 ^o]

1. Find the value of sin2x, sin, cos2x, cos if, cos x = , x lies in third quadrant.
2. Find the principal and general solution of

1. 2sinx + 1 = 0 (b) sin x + cos x=0

1. Find the general solutions for the following

a) sin 2x + sin4x + sin6x = 0

b) 2cos²x + 3sinx = 0

c) cos x + cos3x = 2 - 4sin²x

d) cos x – sin x =

e) sec x + tan x = 1

aditya gupta , 10 Years ago

Grade 11