math_trig_test_question_1$Math\phantom{\rule{0.22em}{0ex}}test\phantom{\rule{0.22em}{0ex}}Paper\phantom{\rule{0.22em}{0ex}}-1$Trigonometry
 Questions Marks Score Q-1Find the principal solutions of cotx=3$\phantom{\rule{0.22em}{0ex}}cotx=\sqrt{3}$ 2 Q-2Find the general solutions of Find general solution of cos 3x= cos 2x$Find\phantom{\rule{0.22em}{0ex}}general\phantom{\rule{0.22em}{0ex}}solution\phantom{\rule{0.22em}{0ex}}of\phantom{\rule{3.3em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}3x=\phantom{\rule{0.22em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}2x$ 2 Q-3Find the general solutions of sin x+sin 3x+sin 5x=0$\phantom{\rule{1.32em}{0ex}}sin\phantom{\rule{0.22em}{0ex}}x+sin\phantom{\rule{0.22em}{0ex}}3x+sin\phantom{\rule{0.22em}{0ex}}5x=0$ 2 Q-4Find the general solutions of cos x-sin x=-1$\phantom{\rule{0.44em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}x-sin\phantom{\rule{0.22em}{0ex}}x=-1$ 2 Q-5aFind the cartesian co-ordinates of point, whose polar coordinates are (2,Ļ2)$\begin{array}{l}Find\phantom{\rule{0.22em}{0ex}}the\phantom{\rule{0.22em}{0ex}}cartesian\phantom{\rule{0.22em}{0ex}}co-ordinates\phantom{\rule{0.22em}{0ex}}of\phantom{\rule{0.22em}{0ex}}point,\phantom{\rule{0.22em}{0ex}}whose\phantom{\rule{0.22em}{0ex}}polar\phantom{\rule{0.22em}{0ex}}\\ coordinates\phantom{\rule{0.22em}{0ex}}are\phantom{\rule{0.22em}{0ex}}\left(2,\frac{\mathrm{Ļ}}{2}\right)\end{array}$ 2 Q-6 aFind the polar co-ordinates of point, whose cartesian coordinates are (1,3)$\begin{array}{l}Find\phantom{\rule{0.22em}{0ex}}the\phantom{\rule{0.22em}{0ex}}polar\phantom{\rule{0.22em}{0ex}}co-ordinates\phantom{\rule{0.22em}{0ex}}of\phantom{\rule{0.22em}{0ex}}point,\phantom{\rule{0.22em}{0ex}}whose\phantom{\rule{0.22em}{0ex}}\\ cartesian\phantom{\rule{0.22em}{0ex}}coordinates\phantom{\rule{0.22em}{0ex}}are\phantom{\rule{0.22em}{0ex}}\left(1,\sqrt{3}\right)\end{array}$ 2 Q-7 Find the general solutions of sin x =tan x$sin\phantom{\rule{0.22em}{0ex}}x\phantom{\rule{0.22em}{0ex}}=tan\phantom{\rule{0.22em}{0ex}}x$ 2 Q-8 Find the general solutions of sin š=sin š¼$sin\phantom{\rule{0.22em}{0ex}}\mathrm{š}=sin\phantom{\rule{0.22em}{0ex}}\mathrm{š¼}$ 3 Q-9 Find the general solutions of cos š=cos š¼$\phantom{\rule{0.22em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}\mathrm{š}=cos\phantom{\rule{0.22em}{0ex}}\mathrm{š¼}$ 3 Q-10 Find the general solutions of tan š=tan š¼$\phantom{\rule{0.22em}{0ex}}tan\phantom{\rule{0.22em}{0ex}}\mathrm{š}=tan\phantom{\rule{0.22em}{0ex}}\mathrm{š¼}$ 3 Q-11Prove that sin2š=sin2š¼ implies š=nšĀ±š¼$Prove\phantom{\rule{0.22em}{0ex}}that\phantom{\rule{0.88em}{0ex}}si{n}^{2}\mathrm{š}=si{n}^{2}\mathrm{š¼}\phantom{\rule{1.1em}{0ex}}implies\phantom{\rule{1.1em}{0ex}}\mathrm{š}=n\mathrm{š}Ā±\mathrm{š¼}$ 3 Q12Prove that cos2š=cos2š¼ implies š=nšĀ±š¼$Prove\phantom{\rule{0.22em}{0ex}}that\phantom{\rule{0.88em}{0ex}}co{s}^{2}\mathrm{š}=co{s}^{2}\mathrm{š¼}\phantom{\rule{1.1em}{0ex}}implies\phantom{\rule{1.1em}{0ex}}\mathrm{š}=n\mathrm{š}Ā±\mathrm{š¼}$ 3 Q13Prove that tan2š=tan2š¼ implies š=nšĀ±š¼ $Prove\phantom{\rule{0.22em}{0ex}}that\phantom{\rule{0.88em}{0ex}}ta{n}^{2}\mathrm{š}=ta{n}^{2}\mathrm{š¼}\phantom{\rule{1.1em}{0ex}}implies\phantom{\rule{1.1em}{0ex}}\mathrm{š}=n\mathrm{š}Ā±\mathrm{š¼}\phantom{\rule{0.22em}{0ex}}$ 3
$\begin{array}{l}Answer-1\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}\frac{5\mathrm{š}}{6},\phantom{\rule{0.22em}{0ex}}\frac{11\mathrm{š}}{6}\\ \\ Answer-2\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=\frac{2n\mathrm{š}}{5}\phantom{\rule{0.66em}{0ex}}or\phantom{\rule{0.22em}{0ex}}x=2m\mathrm{š}\\ \\ Answer-3\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=\frac{n\mathrm{š}}{3},\phantom{\rule{0.22em}{0ex}}x=m\mathrm{š}Ā±\frac{\mathrm{š}}{3}\\ \\ Answer-4\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=2n\mathrm{š}+\frac{\mathrm{š}}{2},\phantom{\rule{0.22em}{0ex}}x=2n\mathrm{š}-\mathrm{Ļ}\\ \\ Answer-5\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.66em}{0ex}}\left(\sqrt{2}\phantom{\rule{0.44em}{0ex}},\phantom{\rule{0.22em}{0ex}}\sqrt{2}\right)\\ \\ Answer-6\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.66em}{0ex}}\left(2\phantom{\rule{0.22em}{0ex}},\phantom{\rule{0.22em}{0ex}}\frac{\mathrm{š}}{3}\right)\\ \\ Answer-7\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=n\mathrm{š}\phantom{\rule{0.66em}{0ex}}or\phantom{\rule{0.44em}{0ex}}x=2m\mathrm{š}\\ \\ Answer-8\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.44em}{0ex}}\mathrm{š}=n\mathrm{š}+\left(-1{\right)}^{n}\mathrm{š¼}\\ \phantom{\rule{0.44em}{0ex}}\\ Answer-9\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.66em}{0ex}}\mathrm{š}=2n\mathrm{š}Ā±\mathrm{š¼}\\ \\ Answer-10\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.44em}{0ex}}\mathrm{š}=n\mathrm{š}+\mathrm{š¼}\\ \end{array}$