If 5sec- 12cosec = 0, find the values of sec, cos and sin.

Given 5sec- 12cosec = 0
5sec = 12cosec
5/cos = 12/sin [sec = 1/cos and cosec = 1/sin]
5/12 = cos/sin
sin/cos = 12/5
tan = 12/5
We know that 1+tan² = sec²
1+(12/5)² = sec²
1+(144/25) = sec²
(25+144)/25 = sec²
169/25 = sec²
Taking square root on both sides
sec = 13/5
cos = 1/sec = 5/13
We know that sin²+cos²=1
sin²+(5/13)² = 1
sin² = 1-(5/13)²
sin² = 1-(25/169)
sin² = (169-25)/169
sin² = 144/169
Taking square root on both sides
sin = 12/13
Hence sec = 13/5 , cos = 5/13 and sin = 12/13.