Question

If cosec theta+cot theta=m and cosec theta-cot theta=n prove that mn=1

Answer 1

Step-by-step explanation:

ANSWER

m

2

n=(cosecθ−sinθ)

2

(secθ−cosθ)=(

sinθ

1−sin

2

θ

)

2

(

cosθ

1−cos

2

θ

)=

sin

2

θcosθ

cos

4

θsin

2

θ

⇒(m

2

n)=cos

3

θ

⇒(m

2

n)

2/3

=cos

2

θ

Similarly mn

2

=(cosecθ−sinθ)(secθ−cosθ)

2

=

cos

2

θsinθ

sin

4

θcos

2

θ

=sin

3

θ

⇒(m

2

n)

2/3

+(mn

2

)

2/3

=sin

2

θ+cos

2

θ=1.