Question

anawer the attachment
qno.74

Answer 1

If x = a secA + b tan A
Y= a tan A + b sec A
To prove x² - y² = a² - b²
Take LHS
x² - y² = (a secA + b tan A)² - (a tan A + b sec A)²
= a² sec²A+ b² tan²A +2(a secA)(b tan A) - [a² tan²A + b²sec²A +2(a tan A)(b secA )]
=a² sec²A+ b² tan²A
+2ab secA tan A
- a² tan²A - b²sec²A
- 2ab tan A secA
= a² sec²A - a² tan²A - b²sec²A + b²
tan²A
=a²(sec²A - tan²A) - b²( sec²A - tan²A)
=a²(1) - b²(1)
= a²- b² = RHS
Hence proved