Question

Which trig expression is equal to sin (72° - a)?

Answer 1

Answer:  The correct option is (C) $\cos(90^\circ-(72^\circ-a)).$

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

$E=\sin(72^\circ-a).$

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

$\sin(90^\circ-x)=\cos x,\\\\\textup{and}\\\\\cos(90^\circ-x)=\sin x.$

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

$E=\sin(72^\circ-a)=\cos(90^\circ-(72^\circ-a)).$

Thus, the correct equivalent expression is $\cos(90^\circ-(72^\circ-a)).$

Option (C) is correct.

Answer 2

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