Question

if √3 tan theta =1 and theta is acute angle find the value sin theta and costheta


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Answer 1

Answer :

• sinθ = 1/2

• cosθ = √3/2

Solution :

• Given : √3•tanθ = 1 , 0 < θ < 90°
• To find : sinθ , cosθ = ?

We have ;

=> √3•tanθ = 1

=> tanθ = 1/√3

Also ,

We know that ,

tanθ = p/b

Thus ,

tanθ = p/b = 1/√3

Clearly ,

p = 1

b = √3

Now ,

As per Pythagoras theorem , we have ;

=> h² = p² + b²

=> h² = 1² + (√3)²

=> h² = 1 + 3

=> h² = 4

=> h = √4

=> h = 2

Thus ,

• sinθ = p/h = 1/2

• cosθ = b/h = √3/2

Alternative method :

We have ,

=> √3•tanθ = 1

=> tanθ = 1/√3

=> tanθ = tan30°

=> θ = 30°

Thus ,

• sinθ = sin30° = 1/2

• cosθ = cos30° = √3/2