Sir please give me a detailed solution of this question as it is taken from trigonometry, topic – trigonometric identities in which we have been given tanθ=1/√5, and we have to find the value of (cosec²θ-sec²θ)/(cosec²θ+sec²θ)
RS Aggarwal, Class 10, chapter 13C, question no 23
tanθ=1/√5
⇒cotθ=√5
∴sec²θ
=(1+tan²θ)
=1+1/5
=6/5
and cosec²θ
=(1+cot²θ)
=1+5
=6
∴(cosec²θ−sec²θ)/(cosec²θ-sec²θ)
=(6-6/5)/(6+6/5)
=24/36
=2/3