Question

In ΔABC, m∠C=90 and m∠A=m∠B,Is cosA=cosB?

Answer 1

Hey there !

Solution:

So we know that in a triangle, the angle sum property of a triangle is 180°.

So it is given that, ∠ A = ∠ B and ∠ C == 90°

So let us take ∠ A to be x

So Applying Angle sum property, we get,

=> ∠ A + ∠ B + ∠ C = 180°

=> X + X + 90 = 180°

=> 2 X = 180 - 90

=> 2 X = 90

=> X = 90 / 2 = 45°

Hence the measure of A and B is 45° as ∠ A = ∠ B.

So we know that Cos 45 = 1 / √2

Hence Cos A = Cos B is true.

Hope my answer helped !

Answer 2

In ∆ABC ,

m<C = 90° ,

and 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

=> x = 45°

Therefore ,

m<A = m<B = 45°

Now ,

Cos A = cos45° = 1/√2 ---( 1 )

Cos B = cos 45° = 1/√2 ---( 2 )

from ( 1 ) and ( 2 ), we get

Cos A = cos B

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