Question

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

Answer 1

`-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)`.