If $$\sin \left( {\theta + {{30}^ \circ }} \right) = \frac{3}{{\sqrt {12} }}{\text{,}}$$ then find $${\text{co}}{{\text{s}}^2}\theta ?$$
A. $$\frac{1}{4}$$
B. $$\frac{3}{4}$$
C. $$\frac{{\sqrt 3 }}{2}$$
D. $$\frac{1}{2}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \sin \left( {\theta + {{30}^ \circ }} \right) = \frac{3}{{\sqrt {12} }} = \frac{3}{{2\sqrt 3 }} \cr & = \frac{{\sqrt 3 }}{2} = \sin \left( {\theta + {{30}^ \circ }} \right) = \sin {60^ \circ } \cr & \therefore \theta = {30^ \circ } \cr & {\text{co}}{{\text{s}}^2}\theta = {\text{co}}{{\text{s}}^2}{30^ \circ } \cr & = {\left( {\frac{{\sqrt 3 }}{2}} \right)^2} \cr & = \frac{3}{4} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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