Ask Me Help Desk - How to prove

Quote:

Originally Posted by prawn

prove : 1/cotA + cosecA = cotA - cosecA

Your formula has an error:

$<br /> \frac 1 {cot(A)} + csc(A) \ne cot(A) - csc(A)<br />$

However, the following is true:

$<br /> \frac 1 {cot(A) + csc(A)} = -(cot(A) - csc(A))<br />$

To prove it start by replacing the cot(A) and csc(A) functions with their sine and cosine equivalents, then simplify - for example on the left hand side multiply numerator and denominator by sin(A).