Question 15

sin 45 deg * cos 45 deg * tan 45 deg = 1/2

The expression evaluates to 1/2 when substituting the trigonometric values of sin 45 degrees, cos 45 degrees, and tan 45 degrees, all of which equal √2/2. Therefore, the product simplifies to (√2/2) * (√2/2) * 1 = 1/2.

A) 1/4

This option is incorrect because the values of sin 45 degrees and cos 45 degrees are both √2/2. Their product, when multiplied by tan 45 degrees (which is 1), results in 1/2, not 1/4.

B) (√2)/4

This choice is also incorrect. The calculation of sin 45 deg * cos 45 deg yields (√2/2) * (√2/2) = 1/2, which does not simplify to (√2)/4.

C) 1/2

This is the correct answer. The product of sin 45 degrees (√2/2), cos 45 degrees (√2/2), and tan 45 degrees (1) results in (√2/2) * (√2/2) * 1 = 1/2.

D) (√2)/2

This option is incorrect because it only represents the value of sin 45 degrees or cos 45 degrees individually. The product of the three trigonometric functions equates to 1/2, not (√2)/2.

E) √2

This option is also incorrect. The result of the expression sin 45 deg * cos 45 deg * tan 45 deg does not yield √2, as the combined product is 1/2.

Conclusion

The correct answer is 1/2, as derived from the multiplication of the trigonometric values associated with 45 degrees. All other options fail to accurately represent the result of the expression based on the fundamental properties of these trigonometric functions.