Prove the following trigonometric identity:

Question

1. cos(π/4 -x)cos(π/4 -y) - sin(π/4 -x)sin(π/4 -y) = sin(x + y)

2. sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x

3. sin² 6x – sin² 4x = sin 2x sin 10x

4. cos² 2x – cos² 6x = sin 4x sin 8x

5. cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)

6. cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

Answer 1

Solution: 1.

soln 2. 

solution 3.

Solution 4.

Solution 5.

Solution 6.