Question

Verify the identity sin(-x)+cot(-x) cos(-x)=-csc(x)

Answer 1

True

Explanation:

The identity is true.

Starting with the left-hand side, we have:

sin(-x) + cot(-x) cos(-x) = sin(-x) + (1/tan(-x)) cos(-x)

Using the trigonometric identity for sin(-x) and cos(-x), we have:

sin(-x) + (1/tan(-x)) cos(-x) = -sin(x) + (1/tan(-x)) (-sin(x))

Using the identity for tan(-x), we have:

-sin(x) + (1/tan(x)) (-sin(x)) = -sin(x) + (-cos(x)/sin(x)) (-sin(x))

Simplifying and using the definition of csc, we have:

-sin(x) + (-cos(x)/sin(x)) (-sin(x)) = -sin(x) - cos(x) = -csc(x)

Thus, the identity sin(-x) + cot(-x) cos(-x) = -csc(x) is true.

Hope this helps!