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if x = asec + btan and y = atono + bsec Prove that x2 -y2 = a2-b2

Posted by Ann Maria 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have,
x = asec{tex}\theta{/tex} + btan{tex}\theta{/tex} and y = atan{tex}\theta{/tex} + bsec{tex}\theta{/tex}
LHS = (x² - y²) = (asec{tex}\theta{/tex} + btan{tex}\theta{/tex})² - (atan{tex}\theta{/tex} + bsec{tex}\theta{/tex})²
= (a²sec²{tex}\theta{/tex} + b²tan²{tex}\theta{/tex} + 2absec{tex}\theta{/tex}tan{tex}\theta{/tex}) - (a²tan²{tex}\theta{/tex} + b²sec²{tex}\theta{/tex} + 2absec{tex}\theta{/tex}tan{tex}\theta{/tex})
= a²(sec²{tex}\theta{/tex} - tan²{tex}\theta{/tex}) - b²(sec²{tex}\theta{/tex} - tan²{tex}\theta{/tex})
= a²- b² = RHS
Therefore, LHS = RHS

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