Question

Cos x + sin x = 1

Please Solve this ..... trigonometry equation

Answer 1

Answer:

Given :

cos x + sin x = 1

In order to solve this first reduce it in form of cos Ф = cos α

Dividing the whole equation by square of coefficient.

i.e.    r = √ 1 + 1 = √ 2

1 / √ 2 cos x + 1 / √ 2 sin x = 1 / √ 2

cos x cos π / 4 + sin x sin π / 4 = cos π / 4

Now above expression is in form :

cos A cos B + sin A sin B = cos ( A - B )

cos ( x + π / 4 ) = cos π / 4

As cos Ф = cos α

then Ф  = ( 2 n π ) ± α   where n ∈ I .

x + π / 4 =  ( 2 n π ) ±  π / 4

Case 1 .

x + π / 4 =  ( 2 m π ) - π / 4

x = ( 2 m π ) - π / 4 -  π / 4

x = ( 2 m π ) - π / 2  where  m ∈ I .

Case 2 .

x + π / 4 =  ( 2 n π ) + π / 4

x =  ( 2 n π ) + π / 4 - π / 4

x =  ( 2 n π )  where  n ∈ I .