Question

Find A if tan 2A = cot (A – 24o)

Answer 1

given : tan 2A = cot ( A - 24)

cot(90-2A)=cot(A-24)

since cot(90- θ)=Tan θ

90-2A= A-24

90+24=A+2A

114= 3A

A= 114/3= 38

therefore A=38

Answer 2

answer : A = 38°

we know, tanx = cot(90° - x)

so, tan2A = cot(90° - 2A) ........(1)

now, tan2A = cot(A - 24°)

from equation (1),

cot(90° - 2A) = cot(A - 24°)

or, 90° - 2A = A - 24°

or, 90° + 24° = 2A + A = 3A

or, 114° = 3A

or, A = 38°

hence, value of A = 38°