Question

if cos A+sin A=√2 cos A then cos A-sinA=​

Answer 1

Answer:

CosA - SinA = √2 SinA

Step-by-step explanation:

Given---> CosA + SinA = √2 CosA

To find ---> Value of ( CosA - SinA )

Solution---> ATQ,

CosA + SinA = √2 CosA

=> SinA = √2 CosA - CosA

Taking CosA common from RHS, we get

=> SinA = ( √2 - 1 ) CosA

Multiplying by ( √2 + 1 ) in whole equation, we get

=> ( √2 + 1 ) SinA = ( √2 + 1 ) ( √2 - 1 ) CosA

We have an identity, a² - b² = ( a + b ) ( a - b ) , applying it here we get,

=> ( √2 + 1 ) SinA = { ( √2 )² - ( 1 )² } CosA

=> √2 SinA + SinA = ( 2 - 1 ) CosA

=> √2 SinA + SinA = ( 1 ) CosA

=> √2 SinA + SinA = CosA

=> √2 SinA = CosA - SinA

=> CosA - SinA = √2 SinA

#Answerwithquality

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