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

Trigonometry Practice Test 1

Question : 4 of 40

Marks: +1, -0

What is the value of

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

Solution:

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

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

=\sin A

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