Answer the following: Find the value of Evaluate cos 15 o –sin 15 o If where α and β are acute angles, show that 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’’ ] 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 ] Find the angle between the hands of a clock at 7:20 P.M. [ ans: 100 o ] If 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 ] If If tan A + cot A = 2, then find tan 100 A + cot 100 A [ans : 2 ] Prove that Prove that tan tan tan tan tan = 1 Prove that cos +cos +cos = Prove that sin 10 o sin 50 o sin 70 o = Prove that cos10 o cos 30 o cos 50 o cos 70 o = Prove that + + = 0 If cosx +cosy = and sinx+siny = tan Prove that Prove that = tanx Prove that cos 5x = 16cos 5 x -20 cos 3 x +5cosx Solve the equation cosx + sin x = cos2x + sin2x Find all values of A between 0 o and 720 o which satisfy the equation 2 cos 2 A -5cosA + 2 = 0 [ans : 60 o , 300 o , 420 o , 660 o ] Find the value of sin2x, sin , cos2x, cos if, cos x = , x lies in third quadrant. Find the principal and general solution of 2sinx + 1 = 0 (b) sin x + cos x=0 Find the general solutions for the following a) sin 2x + sin4x + sin6x = 0 b) 2cos 2 x + 3sinx = 0 c) cos x + cos3x = 2 - 4sin 2 x d) cos x – sin x = e) sec x + tan x = 1

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