Last Updated : 26 Apr, 2019

\\sqrt{\\frac{1+sin\\theta }{1-sin\\theta }}\\:+\\:\\sqrt{\\frac{1-sin\\theta \\:}{1+sin\\theta \\:}} is equal to
(A) 2 secθ
(B) 2 cosθ
(C) 2 sinθ
(D) 2 tanθ


Answer: (A)

Explanation: It can be solved by rationalization
\\frac{\\left(\\sqrt{1+sin\\theta \\:}\\right)^2\\:+\\:\\left(\\sqrt{1-sin\\theta \\:\\:}\\right)^2}{\\sqrt{1-sin^2\\theta \\:\\:}}
Use the property:-
(1-sin2θ = cos2θ)
=\\frac{1\\:+sin\\theta \\:+\\:1\\:-sin\\theta }{cos\\theta }
= 2/cosθ = 2 secθ

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