advance function help?

prove:

tan^2 x - sin^2 x = sin^2 x tan^2 x

thankss alottt

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    LHS = tan² x - sin² x

    = [sin² x / cos²x] - sin² x

    = [sin² x - sin² x . cos² x] / cos² x [Taking a common denominator]

    = [sin² x(1 - cos² x)] / cos² x

    = sin² x . [(1 - cos² x) / cos² x]

    = sin² x . [sin²x / cos² x] [Because sin² x + cos² x = 1]

    = sin² x . tan² x

    = RHS

    So tan² x - sin² x = sin² x . tan² x

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