Question

cosx(tanx+cotx)=

Pls Help

Answer 1

Step-by-step explanation:

Tangent is equal to sine over cosine. Cotangent is equal to cosine over sine. Therefore:

$cos(x)( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )$

Distribute the cos(x) into the sum to get:

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

Get a common denominator by multiplying the first term by sine over sine to get:

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

The numerator adds to equal 1 due to a common trigonometric identity. Therefore the only remaining term is:

$\frac{1}{sin(x)}$

Answer 2

final answer to the expression is csc(x)