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Question

If 2sinα1+cosα+sinα=x, then 1cosα+sinα1+sinα is

A
1x
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B
x
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C
1x
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D
1+x
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Solution

The correct option is B x
2sinα1+cosα+sinα=x

2sinα1+cosα+sinα×(1+sinα)cosα(1+sinα)cosα=x

2sinα(1cosα+sinα)(1+sinα)2cos2α=x

2sinα(1cosα+sinα)1+sin2α+2sinαcos2α=x

2sinα(1cosα+sinα)1+sin2α+2sinα(1sin2α)=x

2sinα(1cosα+sinα)2sin2α+2sinα=x

2sinα(1cosα+sinα)2sinα(2sinα+1)=x

1cosα+sinαsinα+1=x

1cosα+sinα1+sinα=x


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