Question

prove that?,
sin∅-2sin^3∅= tan∅
___________
2cos^∅-cos∅​

Answer 1

Here,

(sin@ - 2sin^3@)

= (sin@ - 2sin@ × sin^2@)

= sin@ ( 1 - 2 sin^2@)

= sin@ ( cos^2@ - sin^2@ )

and

(2cos^3@ - cos@)

= (2cos^2@ × cos@ - cos@)

= cos@ ( 2cos^2@ - 1)

= cos@ ( cos^2@ - sin^2@ )

so,

L.H.S =

(sin@ - 2sin^3@) / (2cos^3@ - cos@)

= sin@ ( cos^2@ - sin^2@ ) / cos@ ( cos^2@ - sin^2@ )

= sin@ / cos@

= tan@

= R.H.S (Proved)