Introduction To Trigonometry
If ∠A and ∠B are acute angles such that cos A = cos B, then show that
∠A = ∠B.
Let us consider a triangle ABC in which CD ⊥ AB.
It is given that
cos A = cos B
We have to prove ∠A = ∠B. To prove this, let us extend AC to P such that BC = CP.
From equation (1), we obtain
By using the converse of B.P.T,
⇒∠ACD = ∠CPB (Corresponding angles) … (3)
And, ∠BCD = ∠CBP (Alternate interior angles) … (4)
By construction, we have BC = CP.
∴ ∠CBP = ∠CPB (Angle opposite to equal sides of a …
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