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4 years ago

Solve 4−|2x−1| = −3

Mathematics

1 answer:

Vanyuwa [196]4 years ago

8 0

<h3>Given</h3>

... 4 - |2x -1| = -3

... x

<h3>Solution</h3>

Add |2x-1|+3

... 7 = |2x-1|

This resolves to two equations:

... -7 = 2x-1

... -6 = 2x

... -3 = x

and ...

... 7 = 2x -1

... 8 = 2x

... 4 = x

The two solutions are x = -3 and x = 4.

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====================================================

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2 years ago

If sin A = 3/8, find the value of cosec A - sec A.

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$\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}$

Step by step explanation:

$\text{Given that,}\\\\~~~~~~\sin A = \dfrac 38 \\\\\implies \sin^2 A = \dfrac 9{64}\\\\\implies 1 - \cos^2 A = \dfrac{9}{64}\\\\\implies \cos ^2 A = 1 - \dfrac 9{64}\\\\\implies \cos^2 A = \dfrac{55}{64}\\\\\implies \cos A =\pm\sqrt{\dfrac{55}{64}}\\ \\\implies \cos A = \pm\dfrac{\sqrt{55}}8\\\\$

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$\text{Now,}\\\\\csc A - \sec A\\\\=\dfrac{1}{\sin A}- \dfrac{1}{\cos A}\\\\=\dfrac 83 -\left(\pm \dfrac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}$

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