Question

Cos (2x-40) °-sin (x-20) °

Answer 1

We all know that sin y =cos (90-y)

sin (x+30) =cos (90-(x+30))

cos 2x=cos (90-(x+30))

This is the type of trigonometric equation

cos x=cos y

Then solution set will be

x=2nπ+y ….(A)

x=2nπ-y. …..(B)

Where n is any integer number.

So will be from (A) Putting x=2x and y=90-(x+30).

2x=2nπ+90-(x+30)=2nπ+60-x

3x=2nπ+60

x=(2nπ+60)/3.

From (B) After putting x=2x and y=90-(x+30) we get

2x=2nπ-(90-(x+30))

2x=2nπ-60+x

x=2nπ-60.