Question

How do I verify #15 using fundamental trig identities?

Answer 1

We start with the more complicated side which is the left side, and show that, on using some trigonometric identities, we will get the term on the right side .

$\frac{sin \theta + tan \theta}{1+cos \theta}$

Using Quotient identity for tangent function, we will get

$\frac{sin \theta+ \frac{sin \theta}{cos \theta}}{1+cos \theta}$

$\frac{sin \theta cos \theta + sin \theta}{cos \theta(1+cos \theta)}$

Taking out sine function from the numerator

$=\frac{sin \theta(1+cos \theta)}{cos \theta(1+cos \theta)}$

Cancelling the common term of numerator and denominator

$=\frac{sin \theta}{cos \theta} = tan \theta$