Final answer:
To solve the trigonometric equation cos x = sin(20 + x)°, we use the complementary nature of sine and cosine. Equating cos x with sin(90 - x)° leads us to find x = 35°, which is the value of x in the given range.
Step-by-step explanation:
To solve the equation cos x = sin(20 + x)° for 0° < x < 90°, we can utilize the fact that cos(θ) = sin(90 - θ) due to the complementary nature of sine and cosine in a right-angled triangle. Since sin(20 + x)° is given to be equal to cos x, and we know that cosine of an angle is equal to the sine of its complement, we can express this equation as:
cos x = sin(90 - x)°
If cos x is equal to sin(90 - x)°, then the angles x and 90 - x must be the same. This yields the following:
x = 90 - x - 20
Solving this equation for x, we get:
2x = 70
x = 35°
Therefore, the value of x is 35° which lies in the given range 0° < x < 90°.
Complete question is:
If cos x = sin(20 + x)° and 0° < x < 90°, then the value of x is