Question

Tan 4 A = cot(A-20) find 3A

Answer 1

GIVEN :

Tan 4A = Cot(A - 20)

Convert Tan 4A in the form of Cot using identities.

Cot ( 90 - 4A ) = Cot ( A - 20 ) [ Tan Ø = Cot ( 90 - Ø )

Cancel Cot on the both sides.

Cot ( 90 - 4A) = Cot ( A - 20 )

90 - 4A = A - 20

90 + 20 = A + 5A

110 = 5A

A = 110/5

A = 22

If A = 22

Then,

3A = 3(22) = 66

Therefore, the value of 3A is 66.

Answer 2

Answer:

given:

Tan 4A = cot(A-20)

according to the question tan and got are the complementary angles so

$4a + (a - 20) = 90$

$4a + a - 20 = 90$

$5a - 20 = 90$

$5a = 90 + 20$

$5a = 110$

$a = 110 \div 5$

$a = 22$

Hence A= 22 degrees so now

3A = 3 × 22

= 66 degrees

$\large\boxed{\fcolorbox{blue}{yellow}{3A= 66 degrees}}$