If secθ + tanθ = x then tanθ =

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KollegeApply · Accepted Answer

Given: sec $\theta$+tan$\theta$=x We know that, sec^2 $\theta$-tan^2 $\theta$=1 $\Rightarrow$ (sec $\theta$+tan $\theta$)(sec $\theta$-tan$\theta$)=1 $\Rightarrow$x(sec $\theta$-tan $\theta$)=1 $\Rightarrow$ sec$\theta$-tan $\theta$=1/x Now, sec$\theta$+tan $\theta$=x, sec $\theta$-tan $\theta$=1/x Subtracting the second equation from the first equation, we get `(sec$\theta$+tan $\theta$)-(sec$\theta$-tan$\theta$)=x-1/x $\Rightarrow$ sec$\theta$+tan$\theta$-sec$\theta$+tan$\theta$=(x^2-1)/x $\Rightarrow$ 2 tan$\theta$=(x^2-1)/x $\Rightarrow$ 2 tan $\theta$=(x^2-1)/(2x) $\Rightarrow$ tan $\theta$=(x^2-1)/(2x)`

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