Cos10 х *cos 7 х -cos 2 x * cos 15 х =0

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To solve this equation, we can start by using the trigonometric identity:

cos(x) * cos(y) = 0.5[cos(x+y) + cos(x-y)]

So the given equation becomes:

0.5[cos(10x+7x) + cos(10x-7x)] - 0.5[cos(2x+15x) + cos(2x-15x)] = 0

Simplify this to get:

0.5[cos(17x) + cos(3x)] - 0.5[cos(17x) + cos(13x)] = 0

Now combine like terms:

0.5[cos(3x) - cos(13x)] = 0

Now, we have that:

cos(3x) - cos(13x) = 0

Using the trigonometric identity:

cos(a) - cos(b) = -2sin[(a+b)/2]sin[(a-b)/2]

We can rewrite the equation as:

-2sin[8x]sin[5x] = 0

Now, we have two cases to consider:

1) sin[8x] = 0
2) sin[5x] = 0

For case 1, sin[8x] = 0 implies that 8x = nπ, where n is an integer.
So, x = nπ / 8

For case 2, sin[5x] = 0 implies that 5x = nπ, where n is an integer.
So, x = nπ / 5

Therefore, the solutions to the given equation are x = nπ / 8 and x = nπ / 5, where n is an integer.