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.
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
= cos (2×45)°
= 0 as the value of cos90° is 0.
Thus the value of cos245° -sin245° is equal to 0.
Q1: What is cos^2x – sin^2x?
Answer: cos2x-sin2x is equal to cos2x.