Question

if angle A and angle B are acute angles such that
tan A= tan B, then show that
angle A= angle B

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Answer 1

$\bf {hello \: dear !!!}$

Solution : - consider a right traingle ABC having two acute angle

°•° TanA = TanB ( Given)

since , BC / AC= AC /BC

=> BC² = AC²

=> BC = AC

so , TanA = 1 and similarly tanB = 1

And as we know that 1 = tan45°

since, tanA = tan45°

A = 45°

Similarly tanB = tan45°

B = 45°

Hence, A = B

$\bf \huge \blue {A\: = B prooved }$
_____________________________

$\bf \pink{hope \: this \: helps \: you}$

$\underline {@rajukumar}$

Answer 2

Answer:

Let us consider a triangle ABC having two acute angles.

now,Tan A = Tan B ( Given )

BC/AC = AC/BC

BC^2 =AC^2

therefore ,BC = AC

Now, we know that in a triangle the angles opposite to the equal sides are equal.

Hence,angle A = angle B

Step-by-step explanation: