Question

if a sin theta =1 and b tan theta =1 , find the relation between a and b​

Answer 1

Answer:

We have ,

L.H.S=

x

2

a

2

−

y

2

b

2

⇒L.H.S=

a

2

sin

2

θ

a

2

−

b

2

tan

2

θ

b

2

[∵x=asinθ,y=btanθ]

⇒L.H.S=

sin

2

θ

1

−

tan

2

θ

1

⇒L.H.S=cosec

2

θ−cot

2

θ [∵1+cot

2

θ=cosec

2

θ∴cosec

2

θ−cot

2

θ=1]

⇒ LHS =1= RHS

Hence, proved

Answer 2

Answer:

sin theta=1/a

cos theta=√(1-sin^2 theta)=√{1-(1/a)^2}

=√{(a^2-1)}/a

b.tan theta=b.sin theta/cos theta

=b.(1/a)/[{a^2-1}/a]

=b/(a^2-1)=1

a^2-1=b

a^2-b=1 is the relationship