Find all solutions to the equation csc x(2sinx-sqrt 2)=0

45° and 135°

Step-by-step explanation:

Given the equation csc x(2sinx-Sqrt 2)=0

This means csc x = 0 and 2sinx-√2 = 0

If 2sinx-√2 = 0, we will have;

2sinx = √2

Dividing both sides of the equation by 2 we have;

2sinx/2 = √2/2

sinx = √2/2

x = arcsin√2/2

x = 45°

Since sin(theta) is also positive in the second quadrant and the angle there is 180-theta, therefore;

x = 180 - 45°

x = 135°

The required solutions are 45° and 135°

Note that csc x = 0 cannot be solved to get x hence, the equation will be ignored.

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