Question 200

If secθ + tanθ = p, (p ≠ 0) then secθ is equal to

Solution

=> $$sec\theta + tan\theta = p$$ --------------Eqn(1)

$$\because$$ $$sec^2\theta - tan^2\theta = 1$$

=> $$(sec\theta + tan\theta)(sec\theta - tan\theta) = 1$$

=> $$(sec\theta - tan\theta) = \frac{1}{p}$$ --------------Eqn(2)

Adding eqns(1)&(2)

=> $$2sec\theta = p + \frac{1}{p} = \frac{p^2 + 1}{p}$$

=> $$sec\theta = \frac{1}{2}[p + \frac{1}{p}]$$

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