If $cosA space equals space 7 over 25 comma$ find the value of (tanA + cotA).

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Solution

Using some figure, we have,

cosA space equals space 7 over 25 space equals space BC over AC

Let, BC = 7K, AC = 25K
Then,

space AB squared space equals space AC squared plus BC squared space space space space space space space equals space left parenthesis 25 straight K right parenthesis squared plus left parenthesis 7 straight K right parenthesis squared space space space space space space space equals space 625 straight K squared minus 49 straight K squared space space space space space space space equals space 576 straight K squared space space space space space space space equals 24 straight K squared semicolon space space So space AB space equals space 24 straight K

Now,

tanA space equals space AB over BC equals fraction numerator 24 straight K over denominator 7 straight K end fraction equals 24 over 7

space space cotA space equals space BC over AB space equals space fraction numerator 7 straight K over denominator 24 straight K end fraction equals 7 over 24

Therefore,

tanA plus cotA space equals space 24 over 7 plus 7 over 24 space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 576 plus 49 over denominator 168 end fraction space space space space space space space space space space space space space space space space space space space space space equals space 625 over 18

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