Question

If cos A= √3/2 Find value of 2 tan A / (1+tan A)(1-tan A)

Answer 1

Answer: root 3

Step-by-step explanation: Given cos a = root 3 / 2

We know that cos a = base / height

Thus base = 3 and height = 2 then by Pythagoras theorem we can find perpendicular

(perpendicular) ^2 + (base) ^2 = (height) ^2

(perpendicular) ^2) = (height) ^2 - ( base) ^2

= (2)^2 - (root 3)^2

= 4-3 = 1

Perpendicular = 1

tan a = perpendicular / base = 1/root3

Putting the value of tan a in eqn

= 2 tan a / ( 1+ tan a) (1-tan a)

= 2 tan a / [1^2 - (tan a) ^2]

=2 * (1/ root 3) / [1 - (1/root3)^2]

= (2 / root 3) / (1-1/3)

= (2/ root 3) / (2/3)

= (2/root 3) *(3/2)

=root 3 ( AS 2 will get cancelled out and 3 as root 3 * root 3 get cancelled out)

= root 3

Answer 2

Answer:

√3

Step-by-step explanation:

cos A = √3/2

cos 60°= √3/2

let us solve,

A = 60°

tan 60°=√3

then,

2tanA/(1+tan A)(1-tan A)...........[1]

putting tan A value in ....[1]

we get,

=2×√3/{1+√3}{1-√3}

=2√3/1-√3+√3-3

=2√3/2+0

=2√3/2

=√3

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hope it helps..☺️