Trigonometry Examples

$\sin (2 x + y)$

Step 1

Apply the sum of angles identity.

$\sin (2 x) \cos (y) + \cos (2 x) \sin (y)$

Step 2

Simplify each term.

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Step 2.1

Apply the sine double-angle identity.

$2 \sin (x) \cos (x) \cos (y) + \cos (2 x) \sin (y)$

Step 2.2

Use the double-angle identity to transform $\cos (2 x)$ to $1 - 2 \sin^{2} (x)$ .

$2 \sin (x) \cos (x) \cos (y) + (1 - 2 \sin^{2} (x)) \sin (y)$

Step 2.3

Apply the distributive property.

$2 \sin (x) \cos (x) \cos (y) + 1 \sin (y) - 2 \sin^{2} (x) \sin (y)$

Step 2.4

Multiply $\sin (y)$ by $1$ .

$2 \sin (x) \cos (x) \cos (y) + \sin (y) - 2 \sin^{2} (x) \sin (y)$