sin 45 deg * cos 45 deg * tan 45 deg =

Rationale

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

The values of sin 45 degrees, cos 45 degrees, and tan 45 degrees are all equal to √2/2. Therefore, when multiplied together, they yield (√2/2) * (√2/2) * 1, which simplifies to 1/2.

A (1/4) YOUR ANSWER

This option represents a value that is too low for the product of the three trigonometric functions. The calculations show that the product of sin 45, cos 45, and tan 45 exceeds 1/4, making this choice incorrect.

B ((√2)/4) YOUR ANSWER

While this option appears to be a fraction involving √2, it does not accurately reflect the multiplication of the three trigonometric functions. The resulting product is not just a simple division of √2, thus making this choice incorrect.

C (1/2) CORRECT

This is the correct answer as detailed above. The product of sin 45 degrees, cos 45 degrees, and tan 45 degrees results in 1/2, confirming that this choice is accurate.

D ((√2)/2) YOUR ANSWER

Although this option is the value of sin 45 degrees and cos 45 degrees individually, it does not account for the multiplication with tan 45 degrees. Therefore, this choice is too low and incorrect.

E (√2) YOUR ANSWER

This option represents a value that is much larger than the product calculated. The multiplication of the three functions does not yield √2, making this choice incorrect.

Conclusion

The calculation of sin 45 deg * cos 45 deg * tan 45 deg leads to 1/2, as derived from the properties of these trigonometric functions. Each function individually equals √2/2, and their product confirms this result. Thus, option C accurately reflects the calculated outcome, while all other choices fail to represent the correct value.

sin 45 deg * cos 45 deg * tan 45 deg =

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

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