Exercise 8.1 Q6 | If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

NCERT Class 10 Maths Chapter 8, Exercise 8.1, Q6: If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

In this video, we solve Question 6 from Exercise 8.1. This is a fundamental proof that connects trigonometric ratios with the geometric properties of triangles—specifically the relationship between equal sides and equal angles.

Step-by-Step Proof Breakdown:
Setup the Triangle: Consider a right-angled triangle ABC, where the right angle is at C. This makes angle A and angle B the two acute angles.

Write the Ratios:

cos A = Adjacent / Hypotenuse = AC / AB

cos B = Adjacent / Hypotenuse = BC / AB

Equate the Given Information: We are given that cos A = cos B.

Therefore, AC / AB = BC / AB

Simplify the Equation: Since the denominators (AB) are the same, they cancel out.

This leaves us with: AC = BC

Apply Geometric Properties: In any triangle, if two sides are equal, the angles opposite to those sides are also equal (Isosceles Triangle Property).

Angle opposite to side BC is ∠A.

Angle opposite to side AC is ∠B.

Final Conclusion: Since AC = BC, it follows that ∠A = ∠B. Proved!

Topics Covered:
Proving angles equal using Trigonometry

Properties of Isosceles Triangles in Trigonometry

NCERT Class 10 Maths Exercise 8.1 Question 6

Understanding "Adjacent" sides for different acute angles

Key Formulas & Rules Used:
cos θ = Base / Hypotenuse

If sides are equal, opposite angles are equal.

Definition of acute angles in a right triangle.

If this proof was easy to follow, please Like the video and Subscribe for the rest of the Chapter 8 solutions!

#Class10Maths #Trigonometry #NCERTSolutions #Chapter8 #Exercise8.1 #MathsProofs #Class10Trigonometry #BoardExam2026 #MathsHelp

Видео Exercise 8.1 Q6 | If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B. канала Gyaani Jagat