Given the expression sin(3x+10°)=cos(2x−10°) , which of the following uses the relationship between the sine and cosine of complementary angles to correctly determine the value of x?

Answer 1

The relationship between the sine and cosine of complementary angles states that for any angle A, sin(A) = cos(90° - A) and cos(A) = sin(90° - A).

In the given expression, sin(3x+10°) = cos(2x - 10°), we can see that the angles inside the sin and cos functions are complementary.

Therefore, we can write:

sin(3x+10°) = sin(90° - (2x - 10°))

Since the sine function is equal, we can equate the angles:

3x + 10° = 90° - (2x - 10°)

Simplifying,

3x + 10° = 90° - 2x + 10°

Combining like terms,

3x + 2x = 90° - 10° - 10°

5x = 70°

Dividing both sides by 5,

x = 14°

Therefore, the correct value of x is 14°.