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STALIN [3.7K]
3 years ago
14

Solve for x the equation 6cos^2 x+4sin^2 x=5.Forex 2 question 6 cos square x + 4 sin square x is equal to 5 ​

Mathematics
1 answer:
DaniilM [7]3 years ago
4 0

Step-by-step explanation:

6 \cos {}^{2} (x)  + 4 \sin {}^{2} (x)  = 5

6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x)  = 5

6 - 6 \sin {}^{2} (x)  + 4 \sin {}^{2} (x)  = 5

6 - 2 \sin { }^{2} (x)  = 5

- 2 \sin {}^{2} (x)  =  - 1

\sin {}^{2} (x)  =  \frac{1}{2}

\sin(x)  =  \frac{1}{ \sqrt{2} }

Take the arc Sine of the function

arcsin( \frac{1}{ \sqrt{2} } ) =  \frac{\pi}{4}

Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)

Use the identity

\sin(x)  =  \sin(x + \pi)

We know that

\sin( \frac{\pi}{4} )  =  \frac{1}{ \sqrt{2} }

so using the identity

\sin( \frac{\pi}{4} + \pi )  =  \sin( \frac{5\pi}{4} )

So we have two answers.

( \frac{\pi}{4} )

( \frac{5\pi}{4} )

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