Question

Find A if tan 2A= cot ( A-24)

Answer 1

tan 2A= cot ( A- 24)

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

90 - 24 = A- 24

90 + 24= 3A

144= 3 A

A= 38

Answer 2

Answer: The measure of angle A is 34°.

Step-by-step explanation:

Since we have given that

$\tan 2A=\cot(A-24)$

We need to find the value of A:

As we know the relation between "Tangent and cotangent" i.e.

$\tan(90^\circ-A)=\cot A$

So, our expression becomes,

$\tan (2A)=cot\ (A-24)\\\\cot\ (90-2A)=\cot\ (A-24)\\\\90-2A=A-24\\\\90+24=A+2A\\\\114=3A\\\\A=\frac{114} {3}\\\\A=38^\circ$

Hence, the measure of angle A is 34°.