Question
If (1+sinθ)/cosθ = x, then find the value of
secθSolution
(1+sinθ)/cosθ = x sinθ/cosθ  + 1/cosθ = x tanθ + secθ =  x  ...........................(i) We know that sec²θ-tan²θ =  1 or (secθ-tanθ)(secθ+tanθ) = 1 or x(secθ-tanθ) = 1 or secθ-tanθ = 1/x ----(2) Subtracting (1) from (2), we will get, 2secθ = x +1/x = (x2+1)/x secθ =  (x2+ 1)/2x
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