Question

Cosx(tanx+cotx)=

Pls Help

Answer 1

Answer:

Answer is csc(x)

Step-by-step explanation:

I convert tan(x)= sin(x)/cos(x) and cot(x)= cos(x)/sin(x).

Then distribute the cos(x).

Then turn it into fractor that has same denominator.

Simplified the numerator sin^2(x)+cos^2(x)=1

$cos(x)*\((tan(x)+cot(x))\\\\cos(x)*(\frac{sin(x)}{cos(x)} +\frac{cos(x)}{sin(x)})\\\\sin(x)+\frac{cos^2(x)}{sin(x)}\\\\sin(x)*\frac{sin(x)}{sin(x)}+\frac{cos^2(x)}{sin(x)}\\\\\frac{sin^2(x)}{sin(x)}+\frac{cos^2(x)}{sin(x)}\\\\\frac{sin^2(x)+cos^2(x)}{sin(x)}\\\\\frac{1}{sin(x)}\\\\csc(x)$

Answer 2

Answer:

→cosecx

Step-by-step explanation:

$\hookrightarrow cosx(tanx+cotx)\\\\\hookrightarrow cosx(\frac{sinx}{cosx} +\frac{cosx}{sinx} )\\\\\hookrightarrow cosx(\frac{sinx \times sinx + cosx \times cosx}{cosx*sinx} )\\\\\hookrightarrow cosx(\frac{sin^{2}x+cosx^{2}x}{cosx*sinx} )\\\\\hookrightarrow cosx(\frac{1}{cosx*sinx} )\\\\\hookrightarrow cosx \times \frac{1}{cosx} \times \frac{1}{sinx} \\\\\hookrightarrow 1\times\frac{1}{sinx} \\\\\hookrightarrow \frac{1}{sinx} \\\\\hookrightarrow cosecx$