Verify the identity:

**tradar** · December 15th 2008, 10:52 AM

1+cscx - cotx = cosx
sec x

**Skalkaz** · December 15th 2008, 10:56 AM

Express every term with certain trigonometric function (e. g. cos(x))

**Mush** · December 15th 2008, 10:57 AM

Originally Posted by tradar

1+cscx - cotx = cosx
sec x

$\frac{1+cosec(x)}{sec(x)} = cos(x) + cot(x)$

$\frac{1+cosec(x)}{sec(x)} = cos(x)(1+\frac{1}{sin(x)})$

$1+cosec(x)= sec(x)cos(x)(1+\frac{1}{sin(x)})$

$1+cosec(x)= \frac{1}{cos(x)}cos(x)(1+cosec(x))$

$1+cosec(x)= 1+cosec(x)$

QED!

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