CBSE Class 10 Answered

sinA-cosA-1/sinA+cosA-1=1/secA-tanA

Asked by skailas803 | 05 Jan, 2023, 11:37: PM

Expert Answer

Let us use the symbol

S = sinA and C = cosA

begin mathsize 14px style fraction numerator sin A minus cos A minus 1 over denominator sin A plus cos A minus 1 end fraction space equals space fraction numerator S minus C minus 1 over denominator S plus C minus 1 end fraction end style

begin mathsize 12px style R H S space equals space fraction numerator S minus C minus 1 over denominator S plus C minus 1 end fraction space equals space fraction numerator S minus left parenthesis C plus 1 right parenthesis over denominator S plus left parenthesis C minus 1 right parenthesis end fraction cross times fraction numerator S minus left parenthesis C minus 1 right parenthesis over denominator S minus left parenthesis C minus 1 right parenthesis end fraction end style

begin mathsize 12px style R H S space equals space fraction numerator S squared plus left parenthesis C squared minus 1 right parenthesis minus S left parenthesis C minus 1 right parenthesis space minus S left parenthesis C plus 1 right parenthesis over denominator S squared minus left parenthesis C minus 1 right parenthesis squared end fraction space equals space fraction numerator negative 2 S C over denominator negative 2 C squared plus 2 C end fraction space equals space fraction numerator S over denominator C minus 1 end fraction end style

( To simplify above expression , we used in numerator " cos²A- 1 = - sin²A " . i.e., C² - 1 = S² "

similarly in denominator , we used " sin²A- 1 = - cos²A " . i.e., S² -1 = -C² )

Hence we get

begin mathsize 14px style fraction numerator sin A minus cos A minus 1 over denominator sin A plus cos A minus 1 end fraction space equals space fraction numerator sin A over denominator cos A minus 1 end fraction end style

If we divide the numerator and denominator of RHS by sinA , we get

begin mathsize 14px style fraction numerator sin A minus cos A minus 1 over denominator sin A plus cos A minus 1 end fraction space equals space fraction numerator 1 over denominator co t A minus cos e c A end fraction end style

( We get RHS of above expression as given above .

we will not get RHS as given in the question , i.e., RHS ≠

begin mathsize 12px style fraction numerator 1 over denominator s e c A space minus space tan A end fraction end style

I cross checked the answer using EXCEL )

Answered by Thiyagarajan K | 06 Jan, 2023, 11:54: AM

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