{\\sqrt{{\cosec} x-1}}/{\\sqrt{{\cosec} x+1}} is equal to

Correct Answer is : secx−tanx

SSC CHSL 19 Mar 2020 Shift 3 Paper

Question : 52 of 100

Marks: +1, -0

{\√{{\cosec} x-1}}/{\√{{\cosec} x+1}}

is equal to

Solution:

Given,

{\√{{\cosec} x-1}}/{\√{{\cosec} x+1}}

On rationalisation,

{\√{{\cosec} x-1}}/{\√{{\cosec} x+1}} \×{\√{{\cosec} x-1}}/{\√{{\cosec} x-1}}

={{\cosec} x-1}/{\√{{\cosec}^{2} x-1}}={{\cosec} x-1}/{\cot x}

[\∵{\cosec}^{2} x-1=\cot ^{2} x]

={{1}/{\sin x}-1}/{{\cos x}/{\sin x}}={1-\sin x}/{\cos x}

={1}/{\cos x}-{\sin x}/{\cos x}=\sec x-\tan x

Go to Question:

Prev Question

Next Question