Question

If tan 2a =cot(a-18)were 2a is an acute angle find the value of a

Answer 1

Here is the solution :

We know that, Tan(90° - A) = cot(A)

Assuming the 18 you gave in the cot function is in degrees,

Tan(2a) = cot(a-18°)

=> Tan(2a) = Tan(90°-(a-18°))

=> Since both are Tan functions and the angles are acute, Definitely the angles in it must be same,

i.e 2a = 90°-a+18°

=> Simplifying

=> 3a = 108°

=> a = 36°

Therefore, Our required value of a is 36°.

if in the given question the 18 is in radians that's another aspect. For that We gotta write the 90° as π/2 and solve for a, And I leave it up to you for practice. As in Most cases the question will only be given in degrees.

Finally, The required value of a is 36°.

Hope you understand, Thanking you,

Bunti 360 !.

Answer 2

Given ::- tan 2A = cot (A-18)

Solution ::-

We know that,

Tan θ = dot (90-θ)

So,

Tan 2A = cot(90 - 2A)

Putting this in given equation,

Tan 2A = cot (A -18)

Cot (90- 2A) = cot (A -18)

(90 -2A) = A -18

90 + 18 = A + 2A

108 = 3A

A = 108/3

A = 36

Therefore the value of A is 36

HOPE IT HELPS YOU!!