How to solve

Question

cos (x+pi/4) - cos (x-pi/4) = sq root of 2?

Answer 1

The trigonometric equation is .

   

.

                                                                           

.

The function sin x  has a period of , first find all solutions in the interval .

The function sin x  is negative in third and fourth quadrant.

In third quadrant,

.

In fourth quadrant,

.

So the solution is .

Finally, add multiples of to each of these solutions to get the general form , where n is an integer.

, where n is an integer.

Comments

The trigonometric equation is sin(x) = - 1.

So looking at the graph of sin x we can see that for the values of x in the range - 4π < x < 4π ;

x = - π/2, 3π/2.

If you want more values for x when sin(x) + 1 = 0, just look at a graph with a larger range.

Finally, add multiples of 2π to each of these solutions to get the general form x = - π/2 + 2nπ and x = 3π/2 + 2nπ, where n is an integer.

The solutions are x = π/2[ 4n - 1 ] and x = π/2[ 4n + 3 ].