Question

If Cosec theta + Cot theta = K then Prove that Sec theta = K2+1/K2-1​

Answer 1

Step-by-step explanation:

Given,

cosecθ+cotθ=k

sinθ1+sinθcosθ=k

sinθ1+cosθ=k

1+cosθ=ksinθ

Squaring both side,

(1+cosθ)2=k2sin2θ

(1+cosθ)2=k2(1−cos2θ)

(1+cosθ).(1+cosθ)=k2(1+cosθ)(1−cosθ)

1+cosθ=k2(1−cosθ)

1+cosθ=k2−k2cosθ

1+(1+k2)cosθ=k2

(1+k2)cosθ=k2−1

cosθ=k2+1k2−1

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