If (cos^2 theta + frac{1}{8} = sin^2 theta), find (tan theta).
-
A.
3 -
B.
(frac{3sqrt{7}}{7}) -
C.
3(sqrt{7}) -
D.
(sqrt{7})
Correct Answer: Option B
Explanation
(cos^2 theta + frac{1}{8} = sin^2 theta)……….(i)
from trigometric ratios for an acute angle, where (cos^{2} theta + sin^2 theta = 1) ……..(ii)
Substitute for equation (i) in (i) = (cos^2 theta + frac{1}{8} = 1 – cos^2 theta )
= (cos^2 theta + cos^2 theta = 1 – frac{1}{8})
(2cos^2 theta = frac{7}{8})
(cos^2 theta = frac{7}{2 times 8})
(frac{7}{16} = cos theta)
(sqrt{frac{7}{16}}) = (frac{sqrt{7}}{4})
but cos (theta) = (frac{text{adj}}{text{hyp}})
(opp^2 = hyp^2 – adj^2)
(opp^2 = 4^2 – (sqrt{7})^{2})
= 16 – 7
opp = (sqrt{9}) = 3
(tan theta = frac{text{opp}}{text{hyp}})
= (frac{3}{sqrt{7}})
(frac{3}{sqrt{7}}) x (frac{sqrt{7}}{sqrt{7}}) = (frac{3sqrt{7}}{7})