Simplify the trigonometric expression

**nando29** · December 15th 2010, 02:00 AM

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

**Prove It** · December 15th 2010, 02:01 AM

$\displaystyle \frac{\cos{\theta}}{\sec{\theta}} + \frac{\sin{\theta}}{\csc{\theta}}= \frac{\cos{\theta}}{\frac{1}{\cos{\theta}}} + \frac{\sin{\theta}}{\frac{1}{\sin{\theta}}}$

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

$\displaystyle = 1$ .

**nando29** · December 15th 2010, 02:09 AM

why is the cos theta not multiplied on the rhs of (sin [theta])/ 1 /(sin [theta])

**Prove It** · December 15th 2010, 02:12 AM

Because it's addition, not multiplication...

**nando29** · December 15th 2010, 02:16 AM

okay, in this example: (a/b/c/d) what would that equal? is it (DA/DB/C) then (CDA/CDB) ?

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