Prove the Double Angle Trigonometric Identities: Step-by-Step Explanation

[Zinab]

Well explained full watch stay connected 👍🏻👍🏻

[Teamstudy]

Super duper easy Just put cos2@ = cos sq theta - sin square theta and write sin sq theta + cos sq theta in place of 1 in RHS and u will get both sides equal in the next step.

[luisalfredonarvaeznarvaez]

Doble angulo demostrado
Fenomenal profesor

[alster]

ALTERNATE (AND FASTER) METHOD

Evaluate the right side instead


sin²x = [1-cos(2x)]/2
sin²x = [1-(1-2sin²x)]/2
sin²x = (2sin²x)/2
sin²x=sin²x

[kiranbarnwal]

Although easy question but nicely explained

[dalemyrie]

I get that same question on a paper when I was doing Advance mathematics some years ago

[Ensign_Cthulhu]

Would you please do a proof of Pythagoras' theorem?

[kainaatmakhani]

AOA sir if you kept captions on so it would be very helpful for all of us?

[mustafizrahman]

Previous problem.
I have solved it in my own approach. Let's see. But let it theta = A. Because I can't write theta.
( 1-2cos^2 A)/(sinA*cosA)
=-(2cos^2A - 1)/(sinA*cosA)
=-cos2A/ sinA*cosA
=-2cos2A/2sinA*cosA
=-2cos2A/sin2A
=-2/(sinA/cosA)
=-2/tan2A
=-2/{2tanA/(1-tan^2 A)}
=(-2+2tan^2 A)/ (2tanA)
=-2/2tan A + (2tan^2 A)/2tanA
=-1/tan A +tan A
=tan A- cot A = tan( theta)-cot( theta). [Showed]
I have solved it like 11th grade (though I am in class 10) but it seems easy to me.

[satyamkumar]

My approch :
We know that cos2 theta = cos^2 theta - sin^2 theta
So, RHS :
1 - (cos^2 theta - sin^2 theta)/2
1 - cos^2 theta + sin^2 theta)/2
And we know, 1 - cos^2 theta = sin^2 theta.
Therefore, sin^2 theta + sin^2 theta/2
2 sin^2 theta/2
=sin^2 theta
So LHS = RHS
Hence, proved

[lazaremoanang]

Lol. It's simple, isn't it? Ok, before having time to watch the video, I can prove it. cos(2a)= cos²a-sin²a= 1-2sin²a <=> sin²a=(1-cos(2a))/2.

[Zinab]

Well explained full watch stay connected 👍🏻👍🏻