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.

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 + tan^{2}x

Hope **Sin2A**, two formulas are helpful.

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