Forum

Trigonometric Functions

Prove the following:
10. sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x
11.
3 3
cos cos 2 sin
4 4
x x x
    π π
+ − − = −        
12. sin2
6x – sin2 4x = sin 2x sin 10x 13. cos2
2x – cos2
6x = sin 4x sin 8x
14. sin2 x + 2 sin 4x + sin 6x = 4 cos2 x sin 4x
15. cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)

Trigonometric Functions

Prove the following:
6. cos cos sin sin sin( )
4 4 4 4
x y x y x y
        π π π π
− − − − − = +                
7.
2
π
tan
4 1 tan
π 1 tan tan
4
x
x
x
x
    +
    +
=       −
  −
 
8.
cos ( ) cos ( ) 2
cot
sin ( ) cos
2
x x
x
x x
π + −
=
  π
π − +    
9.
3π 3π cos cos (2π ) cot cot (2π ) 1

Trigonometric Functions

Find the value of:
(i) sin 75° (ii) tan 15°

Trigonometric Functions

Prove that:-
4.
2 3 2 2
2sin 2cos 2sec 10
4 4 3

Trigonometric Functions

Prove that:
2. 2sin2
6
π
+ cosec2

7 3 2
cos
6 3 2
3. 2 5 2
cot cosec 3tan 6
6 6 6

Trigonometric Functions

Prove that:
1. sin2
π
6
+ cos2
3
π
– tan2
1
–
4 2
π
=

Trigonometric Functions

Prove that sin 5 2sin 3 sin
tan
cos5 cos
x x x
x
x x

Trigonometric Functions

Prove that
cos 7 cos 5
cot
sin 7 – sin 5
x x
x

Trigonometric Functions

Prove that
cos cos 2 cos
4 4
x x x
   

Trigonometric Functions

Show that
tan 3 x tan 2 x tan x = tan 3x – tan 2 x – tan x