Question

Derive the cofunction identity:

a) sin(-x) = cos(90° - x)
a) cos(1) cos(x)
b) cos(x) - sin(x)
c) cos(x) - sin(90° - x)
d) cos(x) + sin(x)

Answer 1

To derive the cofunction identity sin(-x) = cos(90° - x), we can start by rewriting sin(-x) as -sin(x). Then, we use the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b) and plug in the values to simplify and prove the cofunction identity.

Step-by-step explanation:

To derive the cofunction identity, let's start with the given equation sin(-x) = cos(90° - x). We know that sin(-x) is equal to -sin(x), so we can rewrite the equation as -sin(x) = cos(90° - x). Now, we can use the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b). Let a = 90° and b = -x. Plugging in these values, we have -sin(x) = sin(90°)cos(-x) + cos(90°)sin(-x). Since sin(90°) = 1 and cos(90°) = 0, the equation simplifies to -sin(x) = 0 cos(-x) + 1 sin(-x). Simplifying further, we get -sin(x) = sin(-x), which proves the cofunction identity.