Use the information given about the angle \(8,0 \leq 8 \leq 2 \pi\), to find the exact value of the indicated trigonometric function.
\(\operatorname{cod}(2 \theta)=\frac{1}{4}, 0<\theta<\frac{\pi}{2} \quad\) Find \(\cos \theta\)
\(\frac{\sqrt{8-2 \sqrt{10}}}{4}\)
\(\frac{\sqrt{8-2 \sqrt{5}}}{2}\)
\(\frac{\sqrt{6}}{4}\)
\(\frac{\sqrt{10}}{4}\)
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> Given cos 2θ= 1/4
We know cos 2θ= 2cos²θ -1
Or, 1/4 = 2cos²θ -1
Or, 2cos²θ= 1/4 +1=5/4
Or , cos²θ = ⅝
Or , cos θ = √(⅝) = (√5)/(2√2) = (√10)/4
Dipanjan Pati Sun, May 23, 2021 7:15 PM