Question

Write all the other trigonometric ratios of ∠A in terms of sec A.

Answer 1

(i) `sin A  = sin A /1`

= `(sin A ÷ cos A)/(1÷ cos A)`

= `(sin A/cosA)/(1/cosA)`

= `tan A/sec A`

= `sqrt( tan^2 A)/sec A`

= `sqrt(sec^2A-1)/(secA)`

(ii) `cos A =  1/(sec A)`

(iii) `tan A = sqrt(tan^2 A) = sqrt(sec^2 A-1)`

(iv) `cosec  A  = 1/sinA = secA/sqrt(sec^2A-1)`

(v) `cot A = (cos A)/(sin A)`

= `(1/(secA))/(sqrt(sec^2A-1)/secA)`

= `1/(sqrt(sec^2A-1))`