Question

if cosø+cotø=k then prove that cosø=k²-1/k²+1​

Answer 1

Answer:

Given,

cosecθ+cotθ=ksin

1

+

sinθ

cosθ

=k

sinθ

1+cosθ

=k

1+cosθ=ksinθ

Squaring both side,

(1+cosθ)

2

=k

2

sin

2

θ

(1+cosθ)

2

=k

2

(1−cos

2

θ)

(1+cosθ).(1+cosθ)=k

2

(1+cosθ)(1−cosθ)

1+cosθ=k

2

(1−cosθ)

1+cosθ=k

2

−k

2

cosθ

1+(1+k

2

)cosθ=k

2

(1+k

2

)cosθ=k

2

−1

cosθ=

k

2

+1

k

2

−1