Question

Given that: SinA = a/b, then cosecA = a2/b​

Answer 1

Answer:

Given : cosecθ−sinθ=a

3

and secθ−cosθ=b

3

⇒

sinθ

1

−sinθ=a

3

⇒

sinθ

cos

2

θ

=a

3

⇒a=(

sinθ

cos

2

θ

)

3

1

Similarly ; b=(

cosθ

sin

2

θ

)

3

1

⇒a

2

b

2

(a

2

+b

2

)=a

4

b

2

+a

2

b

4

⇒(

sinθ

cos

2

θ

)

3

4

(

cosθ

sin

2

θ

)

3

2

+(

sinθ

cos

2

θ

)

3

2

(

cosθ

sin

2

θ

)

3

4

⇒(cosθ)

8/3−2/3

.(sinθ)

4/3−4/3

+(sinθ)

8/3−2/3

.(cosθ)

4/3−4/3

⇒cos

2

θ+sin

2

θ=1

⇒a

2

b

2

(a

2

+b

2

)=1