Question

If sin x = 4 cos x, then what is (sin x)(cos x)?

a) 1/2
b) 1/4
c) 1/8
d) 1/16

Answer 1

To find the value of (sin x)(cos x), use the given information that sin x = 4 cos x. Substitute this into the expression and solve for cos x using the trigonometric identity sin^2 x + cos^2 x = 1. Substituting this value back into the expression gives the answer of 4/17.

Step-by-step explanation:

To find the value of (sin x)(cos x), we can use the given information that sin x = 4 cos x. We can substitute this into the expression to get:

(sin x)(cos x) = (4 cos x)(cos x) = 4(cos x)*(cos x) = 4(cos x)^2

Since we know that sin^2 x + cos^2 x = 1 (as it is a trigonometric identity), we can solve for cos x using this equation.

1. Solve for sin^2 x using the given information that sin x = 4 cos x:
2. sin^2 x = (4 cos x)^2 = 16 (cos x)^2
3. Use the trigonometric identity sin^2 x + cos^2 x = 1 to solve for cos x:
4. 16 (cos x)^2 + cos^2 x = 1
5. 17 (cos x)^2 = 1
6. (cos x)^2 = 1/17
7. cos x = ± √(1/17)

Substituting this value of cos x back into our expression, we get:

(sin x)(cos x) = 4(cos x)^2 = 4(1/17) = 4/17

Therefore, the correct answer is 4/17.