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2 years ago

15

Write the value of

- 2 \cos {}^{2} c" alt="1 - 2 \cos {}^{2} c" align="absmiddle" class="latex-formula">

1 answer:

enot [183]2 years ago

6 0

Step-by-step explanation:

1-2cos²c.

> (cos²c+sin²c)-2cos²c. (cos²c+sin²c=1)

> cos²c+sin²c-2cos²c

> sin²c-cos²c.

is your correct answer.

hope this helps you.

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

mash [69]

Let $a=\tan A$ and $b=\sin A$ . Then

$m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$

$\implies m^2-n^2=4\tan A\sin A$

and

$mn=(a+b)(a-b)=a^2-b^2$

$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

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3 years ago

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andrew11 [14]

Answer is .5
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lana66690 [7]

Answer:

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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