Question

find the value of tan a whan A is an acute angle and cosec A = 2/ root under 3

Answer 1

tan A= ?
cosec A=2/√3
1 + cot^2A = cosec^2A...........identity
cot^2A = cosec^2A - 1
cot^2A = 4/3 - 1
cot^2A = 1/3
cot A = 1/√3
tan A = 1/cotA
tan A= √3

Answer 2

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we have been given that,

cosec A = 2/√3

squaring both sides

cosec^2 A = 4/3 ........ 1

we know that,

1 + cot^2 A = Cosec^2 A

cot^2 = cosec^2 A - 1

cot^2 A = 4/3 - 1 ( from 1 )

cot^2 A = 1/3

1/tan^2 A = 1/3

tan^2 A = 3

taking square root both sides

tan A = +√3 or -√3

we know that the value of Tan A, where A us an acute angle, can never be negative.

so, Tan A = +√3