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If sec theta +tan theta =m; …

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If sec theta +tan theta =m; & sec theta× tan theta =n; find the value of √mn

Posted by Uallasgowda K R Uallasgowda K R 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Given: (sec{tex}\theta{/tex} + tan{tex}\theta{/tex}) = m and (sec{tex}\theta{/tex} - tan{tex}\theta{/tex}) = n,

LHS = mn = (sec{tex}\theta{/tex} + tan{tex}\theta{/tex})(sec{tex}\theta{/tex} - tan{tex}\theta{/tex})
= sec²{tex}\theta{/tex} - tan²{tex}\theta{/tex} = 1 = RHS [{tex}\because{/tex} sec²{tex}\theta{/tex} - tan²{tex}\theta{/tex} = 1]
{tex}\therefore \sqrt {mn} = 1{/tex}

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