Question

(1-cos2x+sinx)/(sin2x + cos x)=tanx

Answer 1

Hi ...dear..
here is your solution....

Answer 2

$LHS = \frac{(1-cos 2x + sin x )}{(sin 2x + cos x )} \\= \frac{ (2sin^{2} x + sin x )}{ (2sinx cosx + cos x )}$

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We used the following formulae :

1) cos²x - sin² x = cos 2x

=> 1 - sin²x - sin² x = cos 2x

=> 1 - 2sin² x = cos 2x

=> 1 - cos 2x = 2sin² x

2) sin 2x = 2sinxcos x

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$= \frac{sin x (2sin x + 1)}{ cos x (2sin x + 1 )}$

/* After cancellation,we get */

$= \frac{sin x }{cos x }\\= tan x \\= RHS$

$Hence \: proved$

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