Trigonometry Practice Test 1

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Question : 5 of 40

Marks: +1, -0

What is the expression

{\tan x}/{1+\sec x}-{\tan x}/{1-\sec x}

equal to?

cosec x
2 cosec x
2 sin x
2 cos x
None of these

Solution:

{\tan x}/{1+\sec x}-{\tan x}/{1-\sec x}

={\tan x(1-\sec x-1-\sec x)}/{1-\sec^2x}

={\tan x(-2\sec x )}/{\sec^2x-\tan^2x-\sec^2x}

={-2\tan x\sec x}/{-\tan^2x}=2/{\sin x}=2\cosec x

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