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If θ is an acute angle then tanθ + cot θ = 2. Find the value of θ in circular measure. 1. π/62. π/83. π/44. π/12 |
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Answer» Correct Answer - Option 3 : π/4 Given: tanθ + cotθ = 2 θ is an acute angle Concept used: radian measure = (π/180) × degree measure Calculation: tanθ + cot θ = 2 ⇒ tanθ + (1/tanθ ) = 2 Taking LCM, tan2θ + 1 = 2tanθ ⇒ tan2θ + 1 - 2tanθ = 0 ⇒ (tanθ - 1)2 = 0 Taking root on both sides ⇒ tanθ - 1 = 0 ⇒ tanθ = 1 ⇒ θ = 45° Now converting degree to radian Radian measure = 45 × (π/180) ⇒ π/4 ∴ The value of θ in circular measure is π/4. |
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