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Introduction To Trigonometry

Question 6:

If ∠A and ∠B are acute angles such that cos A = cos B, then show that

∠A = ∠B.

Answer:

Let us consider a triangle ABC in which CD ⊥ AB.

It is given that

cos A = cos B

… (1)

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,

CD||BP

⇒∠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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