Let \( \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \in \mathrm{R} \). Then the cubic equation of the type \( a x^{3}+b x^{2}+c x+d=0 \) has either one root real or
\( \mathrm{P} \) all three roots are real. But in case of trigonometric
W) equations of the type \( a \sin ^{3} x+b \sin ^{2} x+c \sin x+d \) \( =0 \) can possess several solutions depending upon the domain of \( \mathrm{x} \).
To solve an equation of the type \( a \cos \theta+\mathrm{b} \sin \theta=\mathrm{c} \). The equation can be written as \( \cos (\theta-\alpha)=\mathrm{c} / \) \( \sqrt{\left(a^{2}+b^{2}\right)} \).
The solution is \( \theta=2 \mathrm{n} \pi+\alpha \pm \beta \), where \( \tan \alpha=b / a \), \( \cos \beta=c / \sqrt{\left(a^{2}+b^{2}\right)} \).
\( |\tan x|=\tan x+\frac{1}{\cos x}(0 \leq x \leq 2 \pi) \) has
(A) no solution
(B) one solution
(C) two solutions
(D) three solutions
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
0