Question

Question 16 (Essay Worth 7 points)

Verify the identity.

tan (x + π/2) = -cot x

Answer 1

Explanation:

We know that tan=sin/cos, so tan(x+π/2)=

`(sin(x+pi/2))/(cos(x+pi/2))`

Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),

so our equation is then

`(sin(x)cos(\pi/2)+cos(x)sin(\pi/2))/(cos(x+\pi/2)) = (cos(x))/(cos(x+\pi/2) )`

Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then

`(cos(x))/(cos(x)cos(\pi/2)-sin(x)sin(\pi/2)) = (cos(x))/(-sin(x)) = -cot(x)`