Question

Solve trigonometric function sin∅ + cos∅ × cot∅

Answer 1

Answer:

$\csc(\theta)$

Step-by-step explanation:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{\cos(\theta)}{\sin(\theta)}$

$\sin^2(\theta)+\cos^2(\theta)=1$

$\implies \sin(\theta)+\cos(\theta)\times\cot(\theta)=\sin(\theta)+\cos(\theta)\times\dfrac{\cos(\theta)}{\sin(\theta)}$

$=\sin(\theta)+\dfrac{\cos^2(\theta)}{\sin(\theta)}$

$=\dfrac{\sin^2(\theta)}{\sin(\theta)}+\dfrac{\cos^2(\theta)}{\sin(\theta)}$

$=\dfrac{\sin^2(\theta)+\cos^2(\theta)}{\sin(\theta)}$

$=\dfrac{1}{\sin(\theta)}$

$=\csc(\theta)$