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12 June, 00:16

Tan (y) + cot (y) / csc (y) = sec (y) prove identity

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  1. 12 June, 00:30
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    [tan (y) + cot (y) ]/csc (y)

    tan (y) = sin (y) / cos (y)

    cot (y) = cos (y) / sin (y)

    csc (y) = 1/sin (y).

    Now rewrite the expression with the equivalent values

    [sin (y) / cos (y) + cos (y) / sin (y) ] / [1/sin (y) ]

    1st, let's work the Numerator only = [sin (y) / cos (y) + cos (y) ].

    = [ (cos² (y) + sin² (y) ] / [cos (y). sin (y) ]

    or (cos² (y) + sin² (y) = 1, →Numerator = 1/[cos (y). sin (y) ]

    Denominator = csc (y) = [1/sin (y) ], Then:

    N/D = 1/[cos (y). sin (y) ] / [1/sin (y) ] = [1 x sin (y) ] / [cos (y). sin (y) ] = 1/cos (y)

    Or 1/cos (y) = sec (y) Q. E. D
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