Question

(cos 15°+ sin 15°)²​

Answer 1

Ответ:

(cos15+sin15)² = cos²15 + 2* cos15 * sin15 + sin²15 = 1 + sin2*15 = 1 + sin30 = 1+ 1/2 = 1 1/2

P. S.  cos²a + sin²a=1

        2*sina * cosa = sin2a  

Answer 2

To simplify the expression (cos 15° + sin 15°)², we can expand it using the binomial theorem:

(a + b)² = a² + 2ab + b²

In this case, a = cos 15° and b = sin 15°. So, let's substitute these values into the formula:

(cos 15° + sin 15°)² = (cos 15°)² + 2(cos 15°)(sin 15°) + (sin 15°)²

Using the trigonometric identity: sin²θ + cos²θ = 1, we can simplify further:

(cos 15° + sin 15°)² = cos² 15° + 2(cos 15°)(sin 15°) + sin² 15°

Since sin²θ + cos²θ = 1, we can replace sin² 15° with (1 - cos² 15°):

cos² 15° + 2(cos 15°)(sin 15°) + sin² 15° = cos² 15° + 2(cos 15°)(sin 15°) + (1 - cos² 15°)

Now, we can combine like terms:

cos² 15° + 2(cos 15°)(sin 15°) + (1 - cos² 15°) = 1 + 2(cos 15°)(sin 15°)

Therefore, (cos 15° + sin 15°)² simplifies to 1 + 2(cos 15°)(sin 15°).