Explain (Question:341032.0)

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TRINA DAS

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· 1 Months ago

Explain (Question:341032.0)

Explain how 4th line comes from 3rd one.

Question:

Find the value of $1 - \frac{s i n^{2} A}{1 + c o s A} + \frac{1 + c o s A}{s i n A} - \frac{s i n A}{1 - c o s A}$

Options:

sin A

cos A

Solution:

$1 - \frac{s i n^{2} A}{1 + c o s A} + \frac{1 + c o s A}{s i n A} - \frac{s i n A}{1 - c o s A}$

$\to 1 - \frac{s i n^{2} A}{1 + c o s A} + \frac{1 - {C O S}^{2} A - {s i n}^{2} A}{s i n A (1 - c o s A)}$

$\to 1 - \frac{s i n^{2} A}{1 + c o s A} + \frac{{{s i n}^{2} A - C O S}^{2} A}{s i n A (1 - c o s A)}$

[ $∴$ 1–cos²A = sin²A]

$\to \frac{1 + c o s A - {s i n}^{2} A}{1 + c o s A} \to \frac{1 + c o s A - (1 - {c o s}^{2} A)}{1 + c o s A}$

$\to \frac{1 + c o s A - 1 - {c o s}^{2} A}{1 + c o s A} \to \frac{c o s A (1 + c o s A)}{(1 + c o s A)}$

$\to C o s A$

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