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If cosecθ = 3x and cotθ = 3/x, then what is the value of x2 - 1/x2?1. 32. 1/33. 94. 1/9 |
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Answer» Correct Answer - Option 4 : 1/9 Given: cosecθ = 3x cotθ = 3/x Formula used: cosec2θ - cot2θ = 1 Calculation: cosecθ = 3x ⇒ cosec2θ = 9x2 [Squaring both sides] .......(1) cotθ = 3/x ⇒ cot2θ = 9/x2 [Squaring both sides] ..........(2) Subtract (2) in (1) cosec2θ - cot2θ = 9x2 - 9/x2 ⇒ 1 = 9(x2 - 1/x2) ⇒ (x2 - 1/x2) = 1/9 ∴ The value of x2 - 1/x2 is 1/9. |
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