Chapter 7: Q.14 (page 473)

Rewrite over a common denominator:
$\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)}$

Short Answer

Expert verified

The simplified expression can be given as $\frac{2}{\sin^{2} (v)}$

Step by step solution

Given information

We are given an expression $\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)}$

On cross multiplying

We get,

$\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)} = \frac{1 + \cos (v) + 1 - \cos (v)}{(1 - \cos (v)) (1 + \cos (v))} = \frac{2}{1 - \cos^{2} (v)} = \frac{2}{\sin^{2} (v)}$

Conclusion

The simplified expression can be given as

$\frac{2}{\sin^{2} (v)}$

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Rewrite over a common denominator:
$\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)}$

Short Answer

Step by step solution

Given information

On cross multiplying

Conclusion

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Rewrite over a common denominator:11-cos(v)+11+cos(v)

Short Answer

Step by step solution

Given information

On cross multiplying

Conclusion

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Rewrite over a common denominator:
$\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)}$