If cosec^{2} \theta(\cos \theta-1)(1+\cos \theta)=k, then what is the value of k ?

SSC CHSL 6 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 75 of 100

Marks: +1, -0

cosec^{2} θ(\cos θ-1)(1+\cos θ)=k

, then what is the value of

k

Solution:

Given,

cosec^{2} θ(\cos θ-1)(1+\cos θ)=k

⇒ \;\; k=cosec^{2} θ[(\cos θ)^{2}-(1)^{2}]

⇒ \;\; k=cosec^{2} θ ×(\cos ^{2} θ-1)

⇒ \;\; k=cosec^{2} θ ×(-\sin ^{2} θ)

⇒ \;\; k=\;{1}/{\sin ^{2} θ} ×(-\sin ^{2} θ)=-1

Go to Question:

Prev Question

Next Question