Math, asked by god55, 10 months ago

If cosec A + cot A =11/2, then tan A is ? I need the answer not any foolish reply​

Answers

Answered by sanketj
0

 =  > cosecx + cotx =  \frac{11}{2}   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: ... \: (i)\\  \\  =  >  {cosec}^{2}  = 1 +  {cot}^{2}x \\  =  >  {cosec}^{2}   -  {cot}^{2} x = 1 \\  =  > (cosecx + cotx)(cosecx - cotx) = 1 \\  =  >  \frac{11}{2} (cosecx - cotx) = 1 \:  \:  \:  \:  \:  \: ... \: (from \: i) \\  =  > cosecx - cotx =  \frac{2}{11} \\  mutiplying \: by \:  - 1 \: throughout \\  =  >   - cosecx + cotx =  -  \frac{2}{11}   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   ... \: (ii) \\  \\  adding \: (i) \: and \:( ii) \\  \\  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  cosecx \:   +   \:  cotx =  \frac{11}{2}  \\  (+) - cosecx + cotx =  -  \frac{2}{11}  \\   -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  \\ 0 + 2cotx =  \frac{11}{2}  -  \frac{2}{11}  \\  =  > 2cotx =  \frac{121 - 4}{22} \\  =  > cotx =  \frac{117}{44}  \\  \\ since \: tanx =  \frac{1}{cotx}  \\ hence \\ tanx =  \frac{44}{117}

Hence, tanx = 44/117.

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