Question

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Answer 1

`cot a = cosA/sinA`
`cot^2A = cos^2A/sin^2A = (1-sin^2A)/sin^2A`
`cot^2A = 1/sin^2A -1=>1+cot^2A = 1/sin^2A `
`sinA = 1/sqrt(1+cot^2A)`
Now,`secA = 1/cosA = 1/sqrt(1-sin^2A)`
`secA = 1/sqrt(1-1/(1+cot^2A))=1/sqrt(cot^2A/(1+cot^2A))`
`secA = sqrt(1+cot^2A)/cotA`
`tanA = 1/cotA`