Question

2(cospi/8+sinpi/8)^2​

Answer 1

Ответ:

Пошаговое объяснение:

2*(cos^2 (pi/8) + sin^2 (pi/8) + 2sin(pi/8) * cos(pi/8)) = 2*(1 + sin(pi/4)) = 2*(2 +√2)/2 = 2 +√2

Answer 2

To simplify the expression $2(\cos(\pi/8) + \sin(\pi/8))^2$, you can use the trigonometric identity:

$\cos^2(\theta) + \sin^2(\theta) = 1$

Let's apply this identity to your expression:

2(\cos(\pi/8) + \sin(\pi/8))^2 &= 2(\cos^2(\pi/8) + 2\cos(\pi/8)\sin(\pi/8) + \sin^2(\pi/8))\\ &= 2(1 + 2\cos(\pi/8)\sin(\pi/8)) \end{align*}\] Now, you can simplify further if you know the values of \(\cos(\pi/8)\) and \(\sin(\pi/8)\). However, these values involve square roots and are not simple to express in terms of basic arithmetic operations. So, the expression \(2(\cos(\pi/8) + \sin(\pi/8))^2\) cannot be simplified into a more straightforward form without using approximate numerical values.