What are the formulae of (1) 1 + cos2x (2) 1 - cos2x

Answer:

Cos (a + b) formula is

Cos (a + b) = Cos a. cos b – Sin a. Sin b………………………..(1)

but when a is same as b then

Cos 2a = Cos a. Cos a – Sin a. Sin a

Cos 2a = Cos2a – Sin2a………………………………………..(2)

We know that

Cos2a + Sin2a = 1………………………………………………….(3)

Consider the given equation 1 + Cos 2x

1 + Cos 2x

From equation (2) we can write it as

1 + Cos 2x = 1 + Cos2x – Sin2x…………………………………(4)

From equation (3) 1 can be written as Cos2x + Sin2x. Substitute in the equation (4)

1 + Cos 2x = Cos2x + Sin2x + Cos2x – Sin2x

1 + Cos 2x = 2Cos2x

Now

1 – Cos 2x = 1 – Cos2x – Sin2x…………………………………(5)

From equation (3) 1 can be written as Cos2x + Sin2x. Substitute in the equation (5)

1 – Cos 2x = Cos2x + Sin2x – Cos2x Sin2x

1 – Cos 2x = 2 Sin2x

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