Question

0%7D%20%20%3D%20%20%5Csin%28x%29%20" id="TexFormula1" title=" \frac{ \sin(x) + \tan(x) }{1 + \sec(x) } = \sin(x) " alt=" \frac{ \sin(x) + \tan(x) }{1 + \sec(x) } = \sin(x) " align="absmiddle" class="latex-formula">
how do I verify this problem?​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Simplify the numerator/denominator using the trigonometric identities

• tanx = $\frac{sinx}{cosx}$ and secx = $\frac{1}{cosx}$

sinx + tanx = sinx + $\frac{sinx}{cosx}$ = $\frac{xsinxcosx+sinx}{cosx}$

= $\frac{sinx(1+cosx)}{cosx}$ ← numerator

and

1 + secx = 1 + $\frac{1}{cosx}$ = $\frac{cosx+1}{cosx}$ ← denominator

Putting this together gives

$\frac{sinx(1+cosx)}{cosx}$ × $\frac{cosx}{1+cosx}$

Cancel cosx and (1 + cosx) on numerator/ denominator, leaving

left side = sinx = right side ⇒ verified