SSC CGL 9 Aug 2015 Shift 2 Paper

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Question : 120 of 200

Marks: +1, -0

If 0° ≤ A ≤ 90°, the simplified form of the given expression sin A cos A (tan A – cot A) is

1
1 – 2 $sin^2$ A
2 $sin^2$ A – 1
1 – $cos^2$ A

Solution:

sin A. cos A (tan A – cot A)
= sin A. cos A

({sinA}/{cosA} - {cosA}/{sinA})

= sin A. cos A

({sin^2 A-cos^2 A}/{sinA.cosA})

=

sin^2

A –

cos^2

A
=

sin^2

A – (1 –

sin^2

A)
=

sin^2

A – 1 +

sin^2

A
= 2

sin^2

A – 1

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