Question

Question 16 (Essay Worth 7 points) Verify the identity. tan (x + π/2) = -cot x

Answer 1

Step-by-step explanation:

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

$\frac{sin(x+pi/2)}{cos(x+pi/2)}$

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

so our equation is then

$\frac{sin(x)cos(\pi/2)+cos(x)sin(\pi/2)}{cos(x+\pi/2)} = \frac{cos(x)}{cos(x+\pi/2) }$

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

$\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)$