If 12cot2θ - 31cosecθ + 32 = 0, 0° < θ < 90° then the value of tanθ will be:
A. $$\frac{4}{3},\,\frac{{3\sqrt 7 }}{7}$$
B. $$\frac{4}{5},\,\frac{{5\sqrt 7 }}{7}$$
C. $$\frac{5}{4},\,\frac{4}{3}$$
D. $$\frac{4}{5},\,\frac{4}{3}$$
Answer: Option A
Solution(By Examveda Team)
12cot2θ - 31cosecθ + 32 = 012cosec2θ - 12 - 31cosecθ + 32 = 0
12cosec2θ - 31cosecθ + 20 = 0
12cosec2θ - 16cosecθ - 15cosecθ + 20 = 0
4cosecθ(3cosecθ - 4) - 5(3cosecθ - 4) = 0
(4cosecθ - 5)(3cosecθ - 4) = 0
cosecθ = $$\frac{5}{4}$$, cosecθ = $$\frac{4}{3}$$
$$ = \frac{{\sqrt 7 \times 3}}{7}$$
Alternate:
Go through option A
12cot2θ - 31cosecθ + 32 = 0
$$\eqalign{ & 12 \times \frac{9}{{16}} - \frac{{31 \times 5}}{4} + 32 = 0 \cr & 0 = 0 \cr} $$
Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
Join The Discussion