3 years ago

A real number between √13 and √14

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

6 0

The real number is 3

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(20 points)Solve the equation cos x = sin (x + 22)

Law Incorporation [45]

Answer:

$\bold{x = 34^\circ}$

Step-by-step explanation:

Given:

$cos x = sin (x + 22^\circ)$

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

$sin(90^\circ-\theta )=cos\theta$

$cos(90^\circ-\theta )=sin\theta$

We can apply above property to solve for $x$ as per given equation.

$cos x = sin (x + 22^\circ)$

Changing $cosx$ to sine form:

$cosx=sin(90^\circ-x)$

$cosx=sin(90^\circ-x) = sin(x+22^\circ)$

$\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}$

So, solution to the equation $cos x = sin (x + 22^\circ)$ is:

$\bold{x = 34^\circ}$

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