Question

If cosec 0 + cote = k, then prove that cos o k-1 k? +1'​

Answer 1

Answer:

Step-by-step explanation:

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

​