Question

Формулы суммы и разницы Cos π/8-sin π/8 Sin a - cos (a-60°) Sin 25° + cos 55° Cos 22°-sin 66°

Answer 1

Ответ:

$1) \cos( \frac{\pi}{8} ) - \sin( \frac{\pi}{8} ) \\ \\ \sqrt{ \frac{1 + \cos( \frac{\pi}{4} ) }{2} } - \sqrt{ \frac{1 - \cos( \frac{\pi}{4} ) }{2} } \\ \\ \sqrt{ \frac{1 + \frac{ \sqrt{2} }{2} }{2} } - \sqrt{ \frac{1 - \frac{ \sqrt{2} }{2} }{2} } \\ \\ \frac{ \sqrt{2 + \sqrt{2} } }{2} - \frac{ \sqrt{2 - \sqrt{2} } }{2} \\ \\ \frac{ \sqrt{2 + \sqrt{2} } - \sqrt{2 - \sqrt{2} } }{2} \\ \\ 2) \sin(a) - \cos(a - 60) \\ \\ \sin(a) - ( \cos(a) \times \cos(60) + \sin(a) \times \sin(60) ) \\ \\ \sin(a) - ( \frac{ \cos(a) }{2} + \frac{ \sqrt{3 } \times \sin(a) }{2} \\ \\ \sin(a) - \frac{ \cos(a) + \sqrt{3} \times \sin(a) }{2}$

$3) \sin(25) + \cos(55) \\ \\ \sin(25) + \cos(90 - 35) \\ \\ \sin(25) + \sin(35) \\ \\ 2 \sin(30) \times \cos( - 5) = \cos(5) \\ \\ \\ 4) \cos(22) - \sin(66) = 0.0136$

~•~•~•ZLOY_TIGROVSKIY~•~•~•

Answer 2

To simplify the expression, let's break it down step by step:

1. Cos π/8 - Sin π/8: This can be simplified using the identity: cos(π/2 - x) = sin(x) So, Cos π/8 - Sin π/8 = sin(π/8)

2. Sin a - cos(a-60°): This can be simplified using the identity: sin(π/2 - x) = cos(x) So, Sin a - cos(a-60°) = cos(60° - a)

3. Sin 25° + cos 55°: We cannot further simplify this expression without additional information since the sine and cosine values of 25° and 55° are specific numerical values.

4. Cos 22° - Sin 66°: We cannot further simplify this expression without additional information since the cosine and sine values of 22° and 66° are specific numerical values.

Now, let's combine the simplified expressions:

sin(π/8) + cos(60° - a) + Sin 25° + cos 55° + Cos 22° - Sin 66°

Please note that if you have specific numerical values for a, 25°, 55°, 22°, and 66°, you can substitute them into the expression to obtain a numerical result. Otherwise, the expression remains in terms of trigonometric functions and variables.