Sin2x formula derivation explained

Learn and know the Sin2x formula in trigonometry. In trigonometric functions chapter this is the one of the important formula. Sin2x has two formulas one is in terms of sin and cos. Another formula is in terms of tan. Sin2x both the formulas we need to learn. Based on the data given in the problem we can use the appropriate formula.

Sin2x formula derivation

Generally, learning and remembering sin2x formula is enough, no need proof. But for better understanding I have given the derivation also. So if you need just go through the derivation otherwise learn directly formula.

Sin2x formula proof (derivation):

We know that,

Sin(A + B) = SinA x CosB + CosA x SinB

Now replace “B” with “A” for getting Sin2A formula

Sin(A + A) = SinA x CosA + CosA x SinA

Sin2A = 2 x SinA x CosA

Finally replace A with x, we get

Sin2x = 2 x Sinx x cosx

Sin2A formula in terms of tan:

Sin2x = 2tanx / 1 + tan2x

Hope Sin2A, two formulas are helpful.

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