Question

Write the expression in terms of sine only. 6(sin(2x)−cos(2x))

Answer 1

To write the expression in terms of sine only, we can use the trigonometric identity cos(2x) = 1 - 2sin^2(x). Therefore, the expression in terms of sine only is 6sin(2x) - 6 + 12sin^2(x).

Step-by-step explanation:

To write the expression in terms of sine only, we can use the trigonometric identity cos(2x) = 1 - 2sin^2(x). So, we have:

6(sin(2x)−cos(2x)) = 6(sin(2x)−(1 - 2sin^2(x)))

Expanding and simplifying further:

6(sin(2x)−cos(2x)) = 6sin(2x) - 6 + 12sin^2(x)

Therefore, the expression in terms of sine only is 6sin(2x) - 6 + 12sin^2(x).

Answer 2

To write the expression in terms of sine only, we can use the identity cos(2x) = 1 - 2sin^2(x). By substituting this identity into the given expression, we can rewrite it as 6sin(2x) - 6 + 12sin^2(x).

Step-by-step explanation:

To write the expression in terms of sine only, we need to eliminate the cosine term. We can do this by using the identity cos(2x) = 1 - 2sin^2(x). Let's substitute this identity into the given expression:

6(sin(2x)−cos(2x)) = 6(sin(2x)−(1 - 2sin^2(x)))

Next, distribute the 6 into each term:

6sin(2x) - 6(1) + 6(2sin^2(x)) = 6sin(2x) - 6 + 12sin^2(x)

This expression is now in terms of sine only.