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

Trigonometric identities are equations that relate different trigonometric functions and are true for all the values that are lies in their domain.

Answer: (1) 1 + cos2x = 2cos²x ,   (2) 1 - cos2x = 2sin²x

Let us see, how to solve.

Explanation:

(1) Use the trigonometric formula, cos(a + b) = cos a cos b – sin a sin b and substitute a = b = x

cos(x + x) = cos x cos x – sin x sin x

cos2x = cos²x - sin²x

Now add 1 on both sides

1 + cos2x = 1 + cos²x - sin²x

Now write cos²x + sin²x for 1 on the right side of the equation, 

1 + cos2x = cos²x + sin²x + cos²x - sin²x

 = 2cos²x

(2) Multiply the equation cos2x = cos²x - sin²x by negative 1 and add 1 on both sides.

-cos2x = - cos²x + sin²x

1 - cos2x = 1 - cos²x + sin²x

Now write cos²x + sin²x for 1 on the right side of the equation,

1 - cos2x = cos²x + sin²x - cos²x + sin²x

= 2sin²x

Thus, 1 + cos2x is 2cos²x  and 1 - cos2x is 2sin²x.