Question

if cosec A + cot A = 3 find the value of tan A​

Answer 1

cosec A + cot A = 3------(1)

we know,

cosec^2A-cot^2A=1

or, (cosecA+cotA)(cosecA-cotA)=1

or, 3(cosecA-cotA)=1

or, cosecA-cotA=1/3 -------(2)

(1) - (2) we get,

2cotA=3-1/3=(9-1)/3=8/3

or, cotA=8/(3×2)=4/3

now, tanA=1/cotA=3/4