(1)/(2) sin 2 x+sin ^2 x-sin x=cos x

Question

(1)/(2) sin 2 x+sin ^2 x-sin x=cos x

Answer 1

To solve the equation

, we can start by simplifying the left-hand side of the equation.First, let's rewrite

as

. This gives us:

Next, we can factor out

from the terms on the left-hand side:

Now, let's consider the possible values of

and

that satisfy this equation.If

, then the equation becomes:

This simplifies to

, which is not true for all values of

.If

, then we can divide both sides of the equation by

:

Now, let's simplify the right-hand side of the equation:

Multiplying both sides by

gives:

Using the Pythagorean identity

, we can rewrite the equation as:

Simplifying further, we get:

This equation is difficult to solve directly, so we can use numerical methods or graphing techniques to find the solutions.By plotting the functions

and

, we can find the points of intersection, which represent the solutions to the equation.After analyzing the graph, we find that the solutions to the equation are:

where

is an integer.Therefore, the correct answer is:

where

is an integer.

Вопрос

(1)/(2) sin 2 x+sin ^2 x-sin x=cos x

Решения

Ответ