Question

Cos^2 41 +sin ^2 30 +sin ^2 41= ​

Answer 1

Ответ:

$\frac{5}{4}$

Пошаговое объяснение:

${\cos}^{2} (41) +{ \sin}^{2} (30) + {\sin}^{2} (41) = \\ = ({\cos}^{2} (41) + {\sin}^{2} (41)) + {\sin}^{2} (30) = \\ = 1 + {( \frac{1}{2}) }^{2} = 1 + \frac{1}{4} = \frac{5}{4}$

Answer 2

To simplify the expression, we'll use the trigonometric identity:

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

So, the given expression becomes:

$\cos^2(41^\circ) + \sin^2(30^\circ) + \sin^2(41^\circ) = 1 + \sin^2(30^\circ) + \sin^2(41^\circ)$

Now, $\sin(30^\circ) = \frac{1}{2}$ and $\sin(41^\circ)$ cannot be simplified further.

Thus, the final result is:

$1 + \frac{1}{4} + \sin^2(41^\circ)$

Keep in mind that $\sin^2(41^\circ)$ is still a value that depends on $\theta$. Without further information or a calculator, we cannot determine the exact numerical value of $\sin^2(41^\circ)$.