Let \( a, b, c, d \in R \). Then the cubic equation of the type \( a x^{3}+b x^{2}+c x+d=0 \) has either one root real or all three roots are real. But in case of trigonometric equations of the type \( a \sin ^{3} x+b \sin ^{2} x+c \sin x+d \)
\( \mathrm{P} \) \( =0 \) can possess several solutions depending upon the domain of \( x \).
To solve an equation of the type \( a \cos \theta+b \sin \theta=c \). The equation can be written as
W \( \cos (\theta-\alpha)=c / \sqrt{\left(a^{2}+b^{2}\right)} \).
The solution is \( \theta=2 \mathrm{n} \pi+\alpha \pm \beta \), where \( \tan \alpha=\mathrm{b} / \mathrm{a}, \cos \beta=\mathrm{c} / \sqrt{\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)} \).
In the interval \( [-\pi / 4, \pi / 2] \), the equation, \( \cos 4 x+\frac{10 \tan x}{1+\tan ^{2} x}=3 \) has
(A) no solution
(B) one solution
(C) two solutions
(D) three solutions
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