Answer:
see explanation
Step-by-step explanation:
using the trigonometric identities
I have used x instead of theta
• sin²x + cos²x = 1
• secx = [tex]\frac{1}{cosx}[/tex] and tanx = [tex]\frac{sinx}{cosx}[/tex]
consider the left side
[tex]\frac{sinx}{cosx}[/tex] + [tex]\frac{cosx}{1+sinx}[/tex]
Combine the fractions
[tex]\frac{sinx(1+sinx)+sos^2x}{cosx(1+sinx)}[/tex]
= [tex]\frac{sinx+sin^2x+cos^2x}{cosx(1+sinx)}[/tex]
= [tex]\frac{1+sinx}{cosx(1+sinx)}[/tex]
= [tex]\frac{1}{cosx}[/tex] = secx = right side → verified
