If 0 ≤ q ≤ 90° and 4 \cos ^{2} \\theta-4 \sqrt{3} \cos \\theta+3=0 then the value of q is

SSC CGL Tier II 12 Apr 2015 Paper

Question : 48 of 100

Marks: +1, -0

If 0 ≤ q ≤ 90° and

4 \cos ^{2} \θ-4 √{3} \cos \θ+3=0

then the value of q is

Solution:

(1)

4 \cos ^{2} \θ-4 √{3} \cos \θ+3=0

⇒(2 \cos \θ)^{2}-2.2 \cos \θ .√{3}+(√{3})^{2}

=0

⇒(2 \cos \θ-√{3})^{2}=0

⇒ 2 \cos \θ-√{3}=0

⇒ 2 \cos \θ=√{3}

⇒ \cos \θ= {√{3}}/{2}=\cos 30°

⇒ \θ=30°

Go to Question:

Prev Question

Next Question