যদি sinθ + cosθ = √3 হয়, তাহলে tanθ + cotθ এর মান কত হবে?
Solution
Correct Answer: Option B
দেওয়া আছে, sinθ + cosθ = √3
⇒ (sinθ + cosθ)2 = (√3)2
⇒ sin2θ + cos2θ + 2sinθ.cosθ = 3
⇒ 1 + 2sinθ.cosθ = 3
⇒ 2sinθ.cosθ = 2
∴ sinθ.cosθ =1
tanθ + cotθ
= sinθ/cosθ + cosθ/sinθ
= (sin2θ + cos2θ)/(sinθ.cosθ)
= 1/1
= 1
⇒ (sinθ + cosθ)2 = (√3)2
⇒ sin2θ + cos2θ + 2sinθ.cosθ = 3
⇒ 1 + 2sinθ.cosθ = 3
⇒ 2sinθ.cosθ = 2
∴ sinθ.cosθ =1
tanθ + cotθ
= sinθ/cosθ + cosθ/sinθ
= (sin2θ + cos2θ)/(sinθ.cosθ)
= 1/1
= 1
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions