Q. 64.2( 342 Votes )

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

Answer :

**To Prove: ∠ A = ∠ B**

**Given: cos A = cos B**

Let there be a right angled triangle ABC, right angled at C.

Now we know that the side opposite to the angle of which we are taking trigonometric ratio is perpendicular, side opposite to right angle is hypotenuse and the side left is base.

So, now let cos of A and B

We know that,

Since for angle A, BC is perpendicular and AC is the base.

Now,

Since for angle B, BC is base and AC is perpendicular.

Given: cos A = cos B

Therefore,

AC = BC

Now, the angles opposite to the equal sides are also equal.

Therefore, ∠A = ∠B

**Hence, Proved.**

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Trigonometric Identities44 mins

Champ Quiz | Trigger on Trigonometry47 mins

Basics of TrigonometryFREE Class

NCERT | Imp. Qs. Discussion - Trigonometry44 mins

NCERT | Imp. Qs. on Trigonometry42 mins

Quiz | Trail of Mixed Questions on Trigonometry59 mins

NCERT | Trigonometric Identities52 mins

NCERT | Discussion on Imp. Qs. of Trignometry45 mins

Champ Quiz | Trigonometry Important Questions33 mins

Solving NCERT Questions on Trigonometric Identities56 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)

NCERT - MathematicsIf, then find the values of sin θ and cos θ.

KC Sinha - MathematicsIf , then find the values of cos θ and sin θ.

KC Sinha - MathematicsIf tan θ =0.75, then find the value of sin θ.

KC Sinha - MathematicsIf , evaluate

(i)

(ii)

KC Sinha - MathematicsIf find the value of cos θ – sin θ.

KC Sinha - MathematicsIf then find the values of sin A + cos A.

KC Sinha - MathematicsIf , then find the values of other t–ratios of angle θ.

KC Sinha - MathematicsIf 15 cot A=18, find sin A and sec A.

KC Sinha - Mathematics