Question

Sin φ cos2 φ +cos φ sin2 φ

Answer 1

Используем формулу синуса суммы:

$\sin\varphi \cos2\varphi +\cos\varphi \sin2\varphi=\sin(\varphi+2\varphi)=\sin3\varphi$

Answer 2

The expression you provided, sin(φ)cos^2(φ) + cos(φ)sin^2(φ), can be simplified using trigonometric identities.

sin(φ)cos^2(φ) + cos(φ)sin^2(φ) is equivalent to sin(φ)(cos^2(φ) + sin^2(φ)).

Now, you can use the trigonometric identity:

cos^2(φ) + sin^2(φ) = 1

So, sin(φ)(cos^2(φ) + sin^2(φ)) simplifies to:

sin(φ)(1)

And finally, sin(φ) times 1 is just equal to sin(φ):

sin(φ)

So, the simplified expression is sin(φ).