Question

(1-sin squared times tan is equal to ?

Answer 1

Recall the important trigonometric identities:

i)
`\sin^2x+\cos^2x=1`

ii)
`\tanx = (\sinx)/(\cosx)`.


We want to simplify
`(1-\sin^2x)\cdot \tanx`.

Since,
`\sin^2x+\cos^2x=1`, then
`1-\sin^2x=\cos^2x`. Thus, the expression


`(1-\sin^2x)\cdot \tanx`
becomes

`\displaystyle{ \cos^2x \cdot (\sin x)/(cosx) = \cos x \sin x.`


Answer:
`\ sinx \ cosx`, or
`\displaystyle{ (\sin2x)/(2)`.