5
If 0° < θ < 90° and 2 sin x + 15 cos2x = 7, then value of tan x -
- A\(\frac{2}{3}\)
- B\(\frac{3}{2}\)
- C\(\frac{3}{4}\)
- D\(\frac{4}{3}\)
Answer not set
Discussion 1
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CCommunity
2 sin x + 15 cos2x = 7
2 sin x + 15(1 - sin2x) = 7
15 sin2x - 2 sin x - 8 = 0
$(sin\;x = \frac{{2 \pm \sqrt {4 + 480} }}{{30}})$
$(sinx = \frac{{2 + 22}}{{30}})$
[only positive value 0 < θ < 90°]
$(sinx = \frac{4}{5})$ ----(i)
$(cosx = \sqrt {1 - {{\left( {\frac{4}{5}} \right)}^2}} = \frac{3}{5})$ ----(ii)
By equation (i) ÷ (ii)
$(tanx = \frac{4}{3})$
2 sin x + 15(1 - sin2x) = 7
15 sin2x - 2 sin x - 8 = 0
$(sin\;x = \frac{{2 \pm \sqrt {4 + 480} }}{{30}})$
$(sinx = \frac{{2 + 22}}{{30}})$
[only positive value 0 < θ < 90°]
$(sinx = \frac{4}{5})$ ----(i)
$(cosx = \sqrt {1 - {{\left( {\frac{4}{5}} \right)}^2}} = \frac{3}{5})$ ----(ii)
By equation (i) ÷ (ii)
$(tanx = \frac{4}{3})$