Question

If x = a secA + b tanA , y = a tanA + b secA ,then prove that : x2 – y2 = a2 – b2

Answer 1

⭐Solution⭐

_

✏given here

X= a sec A +b tan A.....(1)

Y = a tan A + b sec A .....(2)

➡Proved here .

x²-y²= a²-b².

✒we know ,

(x²-y2)

= (x+y)(x-y)

keep value by (1) .and (2)

we get ,

(x²-y²)= [(a sec A +b Tan A )+(b sec A +a tan A )][(a sec A + b tan A )-(a tan A + b sec A)]

= [ (a+b)sec A +(a+b)tan A ] [ (a-b)sec A - (a-b)tan A)]

= [ (a+b)(a-b)(sec²A - tan ²A )]

= (a²-b²)(1)

= (a²-b²)

= R.H.S.

✔Thats Proved .

✏Uses Formula .

♣ (Sec ² A - tan ²A )= 1

♣ (x²-y²)= (x+y)(x-y)

✏Hopes its helps u.