Question

10) If x = a sec and y = b tan , then b2x2-a2y2 ​

Answer 1

Answer:

1

Step-by-step explanation:

ANSWER

b

2

x

2

−a

2

y

2

=a

2

b

2

i) x=asecθ,y=btanθ

LHS=b

2

x

2

−a

2

y

2

=b

2

a

2

sec

2

θ−a

2

b

2

tan

2

θ

=a

2

b

2

(sec

2

θ−tan

2

θ)

=a

2

b

2

=RHS

∵sin

2

+cos

2

θ=1

⇒1−sin

2

θ=cos

2

θ

Dividing both sides by cos

2

θ

⇒sec

2

θ−tan

2

θ=1

(

cosθ

sinθ

=tanθ)

ii) acscθ=x

bcotθ=y

LHS=b

2

x

2

−a

2

y

2

=b

2

a

2

csc

2

θ−a

2

b

2

cot

2

θ

=a

2

b

2

(csc

2

θ−cot

2

θ)

=a

2

b

2

=RHS

∵csc

2

θ

−cot

2

θ

=1