Plzz answer Question no 4
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(cosec²θ - sec²θ) / (cosec²θ + sec²θ)
= (1/sin²θ - 1/cos²θ)/(1/sin²θ + 1/cos²θ)
= (cos²θ - sin²θ)/(cos²θ + sin²θ)
= cos²θ (1-tan²θ)
= (1-tan²θ)/(1+tan²θ)
∵tanθ = 1/√5 ⇒ tan²θ = 1/5
∴(cosec²θ - sec²θ) / (cosec²θ + sec²θ)
= (1-tan²θ)/(1+tan²θ)
= (1-1/5)/(1+1/5) = 4/6 =2/3
= (1/sin²θ - 1/cos²θ)/(1/sin²θ + 1/cos²θ)
= (cos²θ - sin²θ)/(cos²θ + sin²θ)
= cos²θ (1-tan²θ)
= (1-tan²θ)/(1+tan²θ)
∵tanθ = 1/√5 ⇒ tan²θ = 1/5
∴(cosec²θ - sec²θ) / (cosec²θ + sec²θ)
= (1-tan²θ)/(1+tan²θ)
= (1-1/5)/(1+1/5) = 4/6 =2/3
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