Answered

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Determine all solutions to the equation 2cos2 x = 1 − sin x on the interval [0, 2π).

Determine All Solutions To The Equation 2cos2 X 1 Sin X On The Interval 0 2π class=

Sagot :

Given:

Expression as

[tex]2cos^2x=1-sinx[/tex]

To find:

Determine all solutions to the equation.

Explanation:

If

[tex]Sin\theta=Sin\alpha[/tex]

then

[tex]\theta=n\pi+(-1)^n\alpha[/tex]

Solution:

First start as:

[tex]\begin{gathered} 2Cos^2x-1+sinx=0 \\ 1+sinx-2sin^2x=0 \\ sinx=\frac{-1}{2},sinx=1 \end{gathered}[/tex]

So, solution will be

[tex]x=\frac{\pi}{2},\frac{7\pi}{6},\frac{11\pi}{6}[/tex]

Hence, this is the solutions.

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