Question

if cosec theta +cot theta =k, then prove that cos theta= k square - 1 divide by k square +1
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Answer 1

Step-by-step explanation:

ANSWER

Given,

cosecθ+cotθ=k

sinθ

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

The correct option is A

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Answer 2

Answer:

first apply golden rule and make every terms in terms of sin theta and cos theta( golden rule).

1+cos theta/sin theta= k. and then solve it.