Answer: The correct option is (C) [tex]\cos(90^\circ-(72^\circ-a)).[/tex]
Step-by-step explanation: We are given to select the correct trigonometric expression that is equivalent to the following expression:
[tex]E=\sin(72^\circ-a).[/tex]
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
[tex]\sin(90^\circ-x)=\cos x,\\\\\textup{and}\\\\\cos(90^\circ-x)=\sin x.[/tex]
Since (72° - a) is an acute angle, so we must have
[tex]E=\sin(72^\circ-a)=\cos(90^\circ-(72^\circ-a)).[/tex]
Thus, the correct equivalent expression is [tex]\cos(90^\circ-(72^\circ-a)).[/tex]
Option (C) is correct.
