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prakhar raj ratna Grade: 12
        

                                           2sinß




                                    1 + sinß + cosß


 


 


= k


 


then find 


                           1 + sinß - cosß


 




                                 1+ sinß


 

8 years ago

Answers : (1)

askiitianexpert arulmani
6 Points
										

Given : 2 sinß / (1 + sinß + cosß) = k


Multiply numerator & denominator by (1 + sinß - cosß)


We get : 2 sinß (1 + sinß - cosß) / (1 + sinß + cosß) (1 + sinß - cosß)


Denominator is of the form (a + b) (a - b) which is (a^2 - b^2)


Hence this further becomes : 2 sinß (1 + sinß - cosß) / ((1 + sinß)^2 - cos^2ß)


Expanding the denominator, we get : 2 sinß (1 + sinß - cosß) / (1 + sin^2ß + 2sinß - cos^2ß)


Substitute 1 with sin^2ß + cos^2ß in the denominator : 2 sinß (1 + sinß - cosß) / (sin^2ßcos^2ß + sin^2ß + 2sinß - cos^2ß)


Cancelling cos^2ß - cos^2ß, we get : 2 sinß (1 + sinß - cosß) / (sin^2ß + sin^2ß + 2sinß)


Further simplify as : 2 sinß (1 + sinß - cosß) / (2sin^2ß +  2sinß)


=> 2 sinß (1 + sinß - cosß) / 2 sinß (1 +  sinß)


Cancelling 2 sinß from both numerator & denominator, we get : (1 + sinß - cosß) / (1 +  sinß)


Since the given equation is simplified to this form, the value of (1 + sinß - cosß) / (1 +  sinß) IS ALSO "k"


Solution : Given  2 sinß / (1 + sinß + cosß) = k, then (1 + sinß - cosß) / (1 +  sinß) = k



8 years ago
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