1.

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

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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