Which trig expression is equal to sin (72° - a)?
a) cos 18°
b) sin 18°
c) cos (90° - (72° - a))
d) sin (90° - (72° - a ))

 The correct option is (C)

Step-by-step explanation:  We are given to select the correct trigonometric expression that is equivalent to the following expression:

We know that the sine and cosine of any acute angle are complementary to each other.

That is, if 'x' is any acute angle, then

Since (72° - a) is an acute angle, so we must have

Thus, the correct equivalent expression is

Option (C) is correct.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11