Question

Prove that cos ^2A-sin^2A =cos2A

Answer 1

Step-by-step explanation:

Sin^2(theta)+Cos^2(theta)=1 (Trigonomoetric Identity)

Therefore, sin^2(theta)=1-cos^2(theta)

Putting this value into given equation as per question,

we get, sin^2(theta)-cos^2(theta)=1-cos^2(theta)-cos^2(theta)

Thereby, sin^2(theta)-cos^2(theta)=1–2cos^2(theta)

Value of cos theta ranges from 0 to 1. So, in either case, the result can never be equal to 2.

The final result would be ,sin^2(theta)-cos^2(theta)=1–2cos^2(theta) and this is also a well known and widely used trigonometric identity.