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AP EAMCET202120 Aug 2021Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

sinh ( x + y ) cosh ( x - y ) is equal to

Options

  1. A1 2 ( sinh 2 x + sinh 2 y )
  2. B( sinh 2 x + sinh 2 y )
  3. C1 2 ( sinh 2 x - sinh 2 y )
  4. D( sinh 2 x - sinh 2 y )

Correct answer

A. 1 2 ( sinh 2 x + sinh 2 y )

Step-by-step solution

We know, 2 sinh x cosh y = ( sin h ( x + y ) + sin h ( x - y ) ) Or, sinh x cosh y = 1 2 ( sin h ( x + y ) + sin h ( x - y ) ) ⇒ sinh ( x + y ) cosh ( x - y ) = 1 2 [ sin h ( x + y + x - y ) + sin h ( x + y - x + y ) ] = 1 2 ( sin h 2 x + sin h 2 y )

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