Show that - 1-sin A-cos A-cos A-1-sin A-2-cosA

1 + sin A/cos A + cos A/1 + sin A = (1+ sin A)^2 + cos^2 A/(1 + sin A) cos A = 1 + sin^2 A + 2 sin A + cos^2 A /(1 + sin A) cos A = 2 (1 + sin A) /(1 + sin A) ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

Show that : 1...

Question

Show that : $\frac{1 + s i n A}{c o s A} + \frac{c o s A}{1 + s i n A} = \frac{2}{c o s A}$

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Solution

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

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

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

= $\frac{2}{c o s A}$

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Sow that : $\frac{1 + s i n A}{c o s A} + \frac{c o s A}{1 + s i n A} = \frac{2}{c o s A}$

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Show that : 1+sinAcosA+cosA1+sinA=2cosA

1+sinAcosA+cosA1+sinA=(1+sinA)2+cos2A(1+sinA)cosA = 1+sin2A+2sinA+cos2A(1+sinA)cosA = 2(1+sinA)(1+sinA)cosA = 2cosA

Show that : $\frac{1 + s i n A}{c o s A} + \frac{c o s A}{1 + s i n A} = \frac{2}{c o s A}$

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

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

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

= $\frac{2}{c o s A}$