# If , then find the values of cos θ and .

We know that,

Or,

Let,

Side opposite to angle θ = AB = x2 – y2

and Hypotenuse = AC = x2 + y2

In right angled ∆ABC, we have

(AB)2 + (BC)2 = (AC)2 [by using Pythagoras theorem]

(x2 – y2 )2 + (BC)2 = (x2 + y2 )2

(BC)2 = (x2 + y2 )2 – (x2 – y2 )2

Using the identity, a2 – b2 = (a+b)(a – b)

(BC)2 = [(x2 + y2 + x2 – y2 )][ x2 + y2 –( x2 – y2)]

(BC)2 = (2x2)(2y2)

(BC)2 = (4x2y2)

BC =√4x2y2

BC = ±2xy

BC = 2xy [taking positive square root since, side cannot be negative]

and

So,

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Trigonometric Identities33 mins
Trigonometric Identities33 mins
NCERT | Trigonometric Identities52 mins
Quiz | Task on Trigonometric Ratios46 mins
Algebraic Identities48 mins
Quiz | Practice Important Questions on Trigonometrical Identities46 mins
Quiz on Trigonometric Ratios31 mins
T- Ratios of Specified Angles58 mins
Trick to learn all Trigonometric Formulae28 mins
Testing the T- Ratios of Specified Angles57 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Given calculate all other trigonometric ratios.

KC Sinha - Mathematics

If , evaluate

(i)

(ii)

KC Sinha - Mathematics