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Cos2a= 2cos^2a-1 for all values of a

true or false?

User Tobilocker
by
8.1k points

2 Answers

4 votes
True that’s ur answer for ur question
User Tronda
by
8.3k points
2 votes

For the solution/answer of this question, we will use the double angle formula which can be derived as follows:


cos(2a)=cos(a+a)=cos(a)* cos(a)-sin(a)* sin(a)=cos^2(a)-sin^2(a)

Now, the above expression can be simplified to:


cos(2a)=cos^2(a)-sin^2(a)=cos^2(a)-(1-cos^2(a)) (Because
sin^2a=1-cos^2a)

Therefore, we can further simplify it to:


cos(2a)=cos^2a-1+cos^2a=2cos^2a-1 which is the proof which is required.

Thus, we have proved that:


cos(2a)=2cos^2a-1

Thus, this equality is true for all values of a.


User Michael Eden
by
7.6k points

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