1.

If C and Z are acute angles and that cos C = cos Z prove that ∠C = ∠Z

Answer»

Hello mate! Here is your answer.

Kindly PLEASE REFER to the attachment.

I have considered a triangle CAZ where,

  • ∠A = Right angle

  • ∠C and ∠Z = Acute angle

By applying the method of trigonometric ratios and considering the given things:

\implies{\rm} cos C = cos Z

\implies{\rm} AC/CZ = AZ/CZ

\implies{\rm} AC = AZ

As we can see that the opposite and adjacen side to 90° are equal. This says that the triangle assumed is a right-angled isosceles triangle.

In a right-angled isosceles triangle, we know that two angles are always equal (other than 90°). Therefore, we can conclude that:

\implies{\rm} ∠C = ∠Z

Note: You can also use two triangles instead of one triangle and use SIMILARITY criterion method. According to me, this method looks simple!


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