If x = a sec theta + b tan theta and y = a tan theta + b sec theta , prove that x^2- y^2 = a^2- b^2
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Answer :-
→ x² - y² = a² - b² .
Step-by-step explanation :-
We have,
x = a sec ∅ + b tan ∅ .
y = a tan ∅ + b sec ∅ .
°•° x² –y² .
= (a sec ∅ + b tan ∅)² – (a tan ∅ + b sec ∅ )² .
= ( a² sec²∅ + b²tan²∅ + 2 ab sec ∅. tan∅ ) – (a² tan²∅ + b² sec²∅ + 2ab sec ∅. tan∅ ) .
= a² sec²∅ + b² tan²∅+ 2ab sec∅. tan∅ – a²tan²∅ – b²sec²∅ – 2ab sec ∅.tan∅
= a² (sec²∅ – tan²∅ ) + b²(tan²∅ – sec²∅ ) .
= a² – b² .
Hence, it is proved.
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Step-by-step explanation:
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