Simplify- sin 1-cos-1-cos-sin-

The correct option is C 2/sinαsin^2⁡α+(1+cos⁡α )^2/sin⁡α (1+cos⁡α ) =sin^2⁡α+1+2 cos⁡α+ cos^2 α/sin⁡α (1 + cos⁡ α) =2(1+cos⁡α )/sin⁡α (1 + cos⁡ α )=2/sinα ...

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Byju's Answer

Standard XII

Physics

Introduction

Simplify: sin...

Question

Simplify: $\frac{s i n α}{(1 + c o s α)} + \frac{(1 + c o s α)}{s i n α}$

\frac{2}{s i n α}

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2 s i n α

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2 s i n α

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\frac{1}{s i n α}

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Solution

The correct option is A $\frac{2}{s i n α}$
$\frac{s i n^{2} α + (1 + c o s α)^{2}}{s i n α (1 + c o s α)}$ $= \frac{s i n^{2} α + 1 + 2 c o s α + c o s^{2} α}{s i n α (1 + c o s α)}$ $= \frac{2 (1 + c o s α)}{s i n α (1 + c o s α)} = \frac{2}{s i n α}$

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Simplify:sinα(1+cosα)+(1+cosα)sinα

The correct option is A 2sinαsin2α+(1+cosα)2sinα(1+cosα) =sin2α+1+2cosα+cos2αsinα(1+cosα) =2(1+cosα)sinα(1+cosα)=2sinα

Simplify: $\frac{s i n α}{(1 + c o s α)} + \frac{(1 + c o s α)}{s i n α}$

The correct option is A $\frac{2}{s i n α}$
$\frac{s i n^{2} α + (1 + c o s α)^{2}}{s i n α (1 + c o s α)}$ $= \frac{s i n^{2} α + 1 + 2 c o s α + c o s^{2} α}{s i n α (1 + c o s α)}$ $= \frac{2 (1 + c o s α)}{s i n α (1 + c o s α)} = \frac{2}{s i n α}$