Question

if co sec 0- k then prove that cos 0 = k2-1/k2+1​

Answer 1

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

​

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