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Math Help - inverse trigonometry 2

  1. #1
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    inverse trigonometry 2

    show that
    sin-1(3/5) + tan-1(7/24) = cos-1(3/5)

    any help will be greatly appreciated ! thank you!
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  2. #2
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    Quote Originally Posted by iiharthero View Post
    show that
    sin-1(3/5) + tan-1(7/24) = cos-1(3/5)

    any help will be greatly appreciated ! thank you!
    Hint :
    LHS

    1) convert  \sin^{-1} \left (\frac{3}{5} \right ) \ into  \ \tan^{-1}(...)  \ using \ identity
     \sin^{-1} x= \tan^{-1} {\frac{x}{\sqrt{1-x^2}}}

    2) now use identity
     \tan^{-1} {x} + \tan^{-1} {y} = \tan^{-1} { \frac {x+y}{1-xy}}  \quad (if x>0,y>0 & xy<1)

    3)and last, use identity
     \tan^{-1}{x} = \cos^{-1} {\frac{1}{\sqrt{1+x^2}}}
    you will get RHS.
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