Can you show 1 divided by 1 plus cosx equals cscsquaredx minus cscxcotx?

Answer 1

2

Answer 2

take 1 / ( 1 + cos(x)) and multiply top and bottom by (1 - cos(x)), the denominator, when multiplied through, becomes (1 - cos2(x)), which is sin2(x), from the relationship [sin2(x) + cos2(x) = 1], so we have (1 - cos(x)) / sin2(x) = 1 / sin2(x) - (cos(x) / sin2(x)).

1 / sin2(x) = csc2(x), and (cos(x) / sin2(x)) = (1/sin(x))*(cos(x)/sin(x));

cos(x)/sin(x) = cot(x) and (1/sin(x)) = csc(x), so we have csc2(x) - csc(x)*cot(x)