Question

Sin32°cos15°+cos32°sin15°=sin26°cos21°+cos26°x(умножить)sin21° СРОЧНО ХЕЛП

Answer 1

Sin32°cos15°+cos32°sin15°=sin26°cos21°+cos26°sin21°
sin(32°+15°)=sin(26°+21°)
sin47°=sin47°
sin47°-sin47°=0

Answer 2

Calculating Trigonometric Expressions

To solve the given trigonometric expression sin(32°)cos(15°) + cos(32°)sin(15°), we can use the trigonometric identity for the sum of angles: sin(A + B) = sinAcosB + cosAsinB. We can rewrite the expression using this identity.

Using the identity, we get: sin(32°)cos(15°) + cos(32°)sin(15°) = sin(32° + 15°)

Now, let's calculate 32° + 15° to find the equivalent angle.

Calculating the Equivalent Angle

Adding the angles, we get: 32° + 15° = 47°

So, the expression simplifies to: sin(32°)cos(15°) + cos(32°)sin(15°) = sin(47°)

Now, let's calculate the other side of the equation.

Calculating the Other Side of the Equation

The other side of the equation is sin(26°)cos(21°) + cos(26°)sin(21°).

Using the same trigonometric identity, we can rewrite this expression as: sin(26° + 21°)

Adding the angles, we get: 26° + 21° = 47°

So, the other side of the equation simplifies to: sin(26°)cos(21°) + cos(26°)sin(21°) = sin(47°)

Conclusion

Therefore, the given trigonometric expression simplifies to the same value on both sides of the equation: sin(32°)cos(15°) + cos(32°)sin(15°) = sin(26°)cos(21°) + cos(26°)sin(21°) simplifies to sin(47°) = sin(47°).

Hence, the given trigonometric expression is true.