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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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