# Simplify the trigonometric expression

• Dec 15th 2010, 03:00 AM
nando29
Simplify the trigonometric expression
Cos[θ]/Sec[θ] + Sin[θ]/Csc[θ]

the ans = 1

i having trouble with the cancellation of division. showing the steps would help me. thank you
• Dec 15th 2010, 03:01 AM
Prove It
$\displaystyle \frac{\cos{\theta}}{\sec{\theta}} + \frac{\sin{\theta}}{\csc{\theta}}= \frac{\cos{\theta}}{\frac{1}{\cos{\theta}}} + \frac{\sin{\theta}}{\frac{1}{\sin{\theta}}}$

$\displaystyle = \cos^2{\theta} + \sin^2{\theta}$

$\displaystyle = 1$.
• Dec 15th 2010, 03:09 AM
nando29
why is the cos theta not multiplied on the rhs of (sin [theta])/ 1 /(sin [theta])
• Dec 15th 2010, 03:12 AM
Prove It