Formula of cos^2x-sin^2x | cos^2x-sin^2x Formula, Identity

The formula of cos^2x – sin^2x is equal to cos2x. Let us learn how to establish the proof the identity of cos2x-sin2x.

cos2x-sin2x formula is given by cos2x-sin2x = cos2x.

Formula of cos^2x-sin^2x

Proof of cos2x-sin2x Formula

Question: Prove that cos2x-sin2x = cos2x.



= cosx ⋅ cosx – sinx ⋅ sinx

= cos(x+x), here we have used the identity cosa cosb – sina sinb = cos(a+b).

= cos 2x

So cos^2x – sin^2x is equal to cos2x and we have proved this cos2x-sin2x formula by using the identity of cos(a+b).


Question 1: Find the value of cos245° -sin245°.


Putting x=45° in the above formula cos2x-sin2x = cos2x, we obtain that

cos245° -sin245°

= cos (2×45)°

= cos90°

= 0 as the value of cos90° is 0.

Thus the value of cos245° -sin245° is equal to 0.

Related Topics:

1-cos2x FormulaSolutions of sinx=1
sin(pi/2-x) Formula1+cot2x Formula


Q1: What is cos^2x – sin^2x?

Answer: cos2x-sin2x is equal to cos2x.

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