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Please help : Simplify √1-cos²2A/cos(-A).cos(90° + A).​

Please help : Simplify √1-cos²2A/cos(-A).cos(90° + A).​-example-1
User MinuteMed
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1 Answer

2 votes

Answer:


-2,\,\{0^\circ < A < 90^\circ\}

Explanation:


\displaystyle (√(1-\cos^22A))/(\cos(-A)\cos(90^\circ+A))\\\\=(√(\sin^22A))/(\cos(-A)\cos(90^\circ+A))\\\\=(\sin2A)/(\cos(-A)\sin(-A))\\\\=(2\sin A\cos A)/(-\cos(-A)\sin(A))\\\\=(2\cos A)/(-\cos(A))\\\\=-2

Note that by the co-function identity,
\cos(90^\circ+A)=\sin(-A), and that
\cos(-A)=\cos(A) and
\sin(-A)=-\sin(A).

User Francois C
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