Question

I am testing...
who give correct answer will get Brainliest and 1 thanks.
I will post the answer if no one knows.
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Answer 1

Answer:

$y = \frac{1}{2} ln( \frac{1 + sin \: x}{1 - sin \: x} )$

$2y = ln(1 + sin \: x) - ln(1 - sin \: x)$

Differentiating both sides w.r.t x..

$2 \frac{dy}{dx} = \frac{cos \: x}{1 + sin \: x} - \frac{ - cos \: x}{1 - sin \: x} = \frac{cos \: x - sin \: x \: cosx + cosx + sinx \: cosx}{ 1 - {sin}^{2}x } = 2 \frac{cos \: x}{ {cos}^{2}x } = 2 \: sec \: x$

$\frac{dy}{dx} = sec \: x$

Ans.

Answer 2

Answer:

\large{\purple{\sf{2x²-5\sqrt{3}x+4}}}2x²−5

3

x+4

\large{\boxed{\red{\sf{x=\frac{-b±\sqrt{b²-4ac}}{2a}}}}}

x=

2a

−b±

b²−4ac

{\boxed{\sf{x=\frac{-(-5\sqrt{3})±\sqrt{(-5\sqrt{3})²-4(2)(4)}}{2(2)}}}}

x=

2(2)

−(−5

3

)±

(−5

3

)²−4(2)(4)

{\boxed{\sf{x=\frac{5\sqrt{3}±\sqrt{75-32}}{4}}}}

x=

4

5

3

±

75−32

\green{\boxed{\sf{x_{1}=\frac{5\sqrt{3}+\sqrt{43}}{4}}}}

x

1

=

4

5

3

+

43

\green{\boxed{\sf{x_{2}=\frac{5\sqrt{3}-\sqrt{43}}{4}}}}

x

2

=

4

5

3

−

43