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Carlton
Carlton asked in Science & MathematicsMathematics · 5 years ago

please help to solve this 1+sina-cosa/1+sina+cosa=tana/2?

2 Answers

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  • ?
    Lv 6
    5 years ago

    Put s=sina,c=cosa.Then f=(1+s-c)/(1+s+c)=

    (1+s-c)^2/[(1+s)^2-c^2]=[(1+s)^2+c^2-2c(1+s) ]/[1+2s+s^2-c^2]=(2+2s-2c-2sc)/[2s(s+1)]=

    [(1-c)+s(1-c)]/[s(s+1)]=(1-c)(1+s)/[s(s+1)]=(1-c)/s Now c=1-2sin^2(a/2) & s=2sin(a/2)* cos(a/2) so f=2sin^2(a/2)/[2sin(a/2)cos(a/2)]=

    tan(a/2). This was an identity. Nothing to solve, just to prove. QED.

  • Iggy Rocko
    Lv 7
    5 years ago

    Solve the equation or verify the identity?

    I suspect the equation is missing parentheses. You'll need to provide them.

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