If sec $\theta$ + tan $\theta$ = x, then sec $\theta$ =

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KollegeApply · Accepted Answer

Given: sec $\theta$+tan $\theta$=1 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 =x sec $\theta$-tan $\theta$=1/x Adding the two equations, 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 sec $\theta$=(x^2+1)/x $\Rightarrow$ sec $\theta$=(x^2+1)/(2x)`

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