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November 23, 2014

November 23, 2014

Posted by **wruck** on Wednesday, June 2, 2010 at 6:10pm.

csc(x)+sec(x)/sin(x)+cos(x)=cot(x)+tan(x)

the left side of the equation is all one term.

- Trig: use parentheses -
**MathMate**, Wednesday, June 2, 2010 at 7:37pmVerify:

(csc(x)+sec(x))/(sin(x)+cos(x))=cot(x)+tan(x)

Left hand side

(csc(x)+sec(x))/(sin(x)+cos(x))

=(1/sin(x)+1/(cos(x))/(sin(x)+cos(x))

=((cos(x)+sin(x))/(sin(x)cos(x))/(sin(x)+cos(x))

=1/(sin(x)cos(x))

Right hand side:

cot(x)+tan(x)

=cos(x)/sin(x) + sin(x)/cos(x)

=(cos²(x) + sin²(x))/(sin(x)+cos(x))

=1/(sin(x)+cos(x))

So the identity is verified.

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