Answer:
see explanation
Step-by-step explanation:
Consider the left side
Simplify the numerator/denominator using the trigonometric identities
• tanx = [tex]\frac{sinx}{cosx}[/tex] and secx = [tex]\frac{1}{cosx}[/tex]
sinx + tanx = sinx + [tex]\frac{sinx}{cosx}[/tex] = [tex]\frac{xsinxcosx+sinx}{cosx}[/tex]
= [tex]\frac{sinx(1+cosx)}{cosx}[/tex] ← numerator
and
1 + secx = 1 + [tex]\frac{1}{cosx}[/tex] = [tex]\frac{cosx+1}{cosx}[/tex] ← denominator
Putting this together gives
[tex]\frac{sinx(1+cosx)}{cosx}[/tex] × [tex]\frac{cosx}{1+cosx}[/tex]
Cancel cosx and (1 + cosx) on numerator/ denominator, leaving
left side = sinx = right side ⇒ verified
