What is the simplest value of \frac{(1-\sin A\cos A)(\sin^2A-\cos^2A)}{\cos A(\sec A-\cosec A)(\sin^3A+\cos^3A)}?

Trigonometry Practice Test 1

Question : 14 of 40

Marks: +1, -0

What is the simplest value of

{(1-\sin A\cos A)(\sin^2A-\cos^2A)}/{\cos A(\sec A-\cosec A)(\sin^3A+\cos^3A)}

Solution:

{(1-\sin A\cos A)(\sin^2A-\cos^2A)}/{\cos A(\sec A-\cosec A)(\sin^3A+\cos^3A)}

={(1-\sin A\cos A)(\sin A-\cos A)(\sin A+\cos A)}/{\cos A( 1/{\cos A}-1/{\sin A})(\sin A+\cos A)(\sin^2A+\cos^2A-\sin A\cos A)}

={(1-\sin A\cos A)(\sin A-\cos A)(\sin A\cos A) }/{\cos A( \sin A-\cos A) (1-\sin A\cos A)}

=\sin A

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