Question

(cosα/sin2α+sinα/cos2α)∙sin4α/cosα

Answer 1

Ответ:

решение смотри на фотографии

Объяснение:

Answer 2

Let's break down the expression step by step:

1. $\frac{\cos \alpha}{\sin^2 \alpha} + \frac{\sin \alpha}{\cos^2 \alpha}$: This is a combination of two fractions with trigonometric functions in the numerator and denominator. To simplify it, let's find a common denominator and add the fractions together.

   We can start by multiplying the first fraction by $\frac{\cos \alpha}{\cos \alpha}$ and the second fraction by $\frac{\sin \alpha}{\sin \alpha}$ to get a common denominator of $\sin^2 \alpha \cos^2 \alpha$:

   $\frac{\cos^2 \alpha}{\sin^2 \alpha \cos \alpha} + \frac{\sin^2 \alpha}{\sin \alpha \cos^2 \alpha}$

   Now, we can add the fractions:

   $\frac{\cos^2 \alpha + \sin^2 \alpha}{\sin^2 \alpha \cos \alpha}$

   Since $\cos^2 \alpha + \sin^2 \alpha = 1$ (trigonometric identity), the expression simplifies to:

   $\frac{1}{\sin^2 \alpha \cos \alpha}$

2. $\frac{\sin^4 \alpha}{\cos \alpha}$: This is a single fraction with trigonometric functions in the numerator and denominator.

Now, let's multiply the simplified result from step 1 with the fraction from step 2:

$\frac{1}{\sin^2 \alpha \cos \alpha} \cdot \frac{\sin^4 \alpha}{\cos \alpha}$

Multiplying these fractions gives:

$\frac{\sin^4 \alpha}{\sin^2 \alpha \cos^2 \alpha}$

Since $\sin^2 \alpha = 1 - \cos^2 \alpha$ (trigonometric identity), we can substitute this value into the denominator:

$\frac{\sin^4 \alpha}{(1 - \cos^2 \alpha) \cos^2 \alpha}$

Now, using the trigonometric identity $\sin^2 \alpha = 1 - \cos^2 \alpha$ once again, we get:

$\frac{\sin^4 \alpha}{\cos^2 \alpha - \cos^4 \alpha}$

This is the simplified expression for the given expression $\frac{\cos \alpha}{\sin^2 \alpha} + \frac{\sin \alpha}{\cos^2 \alpha} \cdot \frac{\sin^4 \alpha}{\cos \alpha}$.