cos(x+y).cos(x-y)=cos^2y-sin^2x
Answers
Answered by
47
here is your solution mate, Hope it's helpful to you!!!
Attachments:
Answered by
51
Answer:
Cos(x + y)Cos(x - y) = Cos²y - Sin²x
Step-by-step explanation:
Cos(x + y)Cos(x - y) = Cos²y - Sin²x
LHS
= Cos(x + y)Cos(x-y)
Using Formuls
Cos(a + b) = CosACosb + SinaSinb
Cos(a - b) = CosACosb - SinaSinb
= (CosxCosy + SinxSiny)(CosxCosy - SinxSiny)
using (a + b) (a - b) = a² - b²
= (CosxCosy)² - (SinxSiny)²
= Cos²xCos²y - Sin²xSin²y
= Cos²y(1 - Sin²x) - (1 - Cos²y)Sin²x
= Cos²y - Cos²ySin²x - Sin²yx + Cos²ySin²x
= Cos²y - Sin²x
= RHS
QED
Proved
Cos(x + y)Cos(x - y) = Cos²y - Sin²x
Similar questions
Science,
6 months ago
Math,
6 months ago
Math,
6 months ago
Political Science,
1 year ago
Math,
1 year ago