Question

In ΔABC, m∠C=90 and m∠A=m∠B,Is tanA=tanB?

Answer 1

In case that C is obtuse,

 

Then C>90.

So A+B msut be less than 90... (because in a triangle A+B+C=180, and C is above 90)

So tan(A+B) must be postivie... (Since A+B is acute < 90)

tan(A+B) = (tanA+tanB)/(1-tanAtanB)

So 1-tanAtanB>0..... (Only then tan(A+B) can be positive)

Hence tanAtanB<1

Answer 2

In ∆ABC ,

m<C = 90°

m<A = m<B = x ,

m<A + m<B + m<C = 180°

[ Angle sum property ]

=> x + x + 90° = 180°

=> 2x = 180° - 90°

=> 2x = 90°

=> x = 90°/2 = 45°

Therefore ,

m<A = m<B = 45°

Now ,

tan A = tan 45° = 1 ----( 1 )

tan B = tan 45° = 1 ----( 2 )

From ( 1 )& ( 2 ), we get

tan A = tan B

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