Question

Find A, if tan3A = cot2A, where 3A and 2A are acute angles.

Answer 1

ANSWER

given

tan3A = tan2A

3A and 2A are acute angles

CONCEPT

• note that for x belongs to (-π/2,π/2)

tan^-1( tanx) = x

• and for x belongs to (0, π) cot^-1(cotx) = x
• since 3A and 2A are acute angles means not negative also less then 90
• also, tanx = cot(90-x)
• and cotx = tan(90-x)
• at 90 degree function changes value

SOLUTION

tan3A = cot2A

cot(90-3A) = cot2A

90-3A = cot^-1( cot2A)

90-3A = 2A

A = 90/5

A = 18

hope it helps

Answer 2

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