Question

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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

assume # to be theta

LHS = ( sin # - 2 sin³ # ) / ( 2 cos³# - cos # )

= ( sin # { 1 - 2 sin²# } ) / ( cos # { 2 cos²# - 1 } )

= ( sin #{ sin²# + cos²# - 2 sin²# } ) / ( cos # { 2 cos² # - [sin² # + cos²# ] } )

=  ( sin #{ sin²# + cos²# - 2 sin²# } ) / ( cos # { 2 cos² # - sin² # - cos²#  } )

                              because 1 = sin²# + cos² #

= ( sin # { cos²# - sin²# } ) / ( cos #  { cos²# - sin²# } )

{ cos²# - sin²# } and { cos²# - sin²# } will be cancelled in numerator and denominator

= sin # / cos #

= tan #

= RHS

hence proved