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Question Number 58312    Answers: 0   Comments: 4

Show that the angle θ between two unit vectors a_ ^ and b_ ^ is given by cosθ=a_ ^ •b_ ^ . Hence, given that a_ ^ =i_ cosA+j_ sinA and b_ ^ =i_ cosB−j_ sinB, prove that cos(A+B)= cosAcosB−sinAsinB.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angle}\:\theta\:\mathrm{between}\:\mathrm{two}\:\mathrm{unit} \\ $$$$\mathrm{vectors}\:\underset{} {\hat {\mathrm{a}}}\:\mathrm{and}\:\underset{} {\hat {\mathrm{b}}}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{cos}\theta=\underset{} {\hat {\mathrm{a}}}\bullet\underset{} {\hat {\mathrm{b}}}. \\ $$$$\mathrm{Hence},\:\mathrm{given}\:\mathrm{that}\:\underset{} {\hat {\mathrm{a}}}=\underset{} {\mathrm{i}cosA}+\underset{} {\mathrm{j}sinA}\:\mathrm{and} \\ $$$$\underset{} {\hat {\mathrm{b}}}=\underset{} {\mathrm{i}cosB}−\underset{} {\mathrm{j}sinB},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{cos}\left(\mathrm{A}+\mathrm{B}\right)= \\ $$$$\mathrm{cosAcosB}−\mathrm{sinAsinB}. \\ $$

Question Number 58313    Answers: 2   Comments: 2

Question Number 54334    Answers: 1   Comments: 1

Question Number 54322    Answers: 3   Comments: 0

Question Number 54312    Answers: 1   Comments: 2

Question Number 54289    Answers: 2   Comments: 5

Question Number 54286    Answers: 2   Comments: 2

Question Number 54281    Answers: 0   Comments: 1

Question Number 54278    Answers: 0   Comments: 4

If f be n→n (n∈N) and is increasing, f(f(n))=3n; find f(2). options: 1, 2, 3,4 .

$${If}\:{f}\:{be}\:{n}\rightarrow{n}\:\:\:\left({n}\in\mathbb{N}\right)\:{and}\:{is}\:{increasing}, \\ $$$${f}\left({f}\left({n}\right)\right)=\mathrm{3}{n};\:{find}\:{f}\left(\mathrm{2}\right). \\ $$$${options}:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\mathrm{4}\:. \\ $$

Question Number 54271    Answers: 1   Comments: 1

Question Number 54270    Answers: 2   Comments: 0

Find the equation to two circles which touch the x−axis at the origin and also touch the line 12x+5y=60

$${Find}\:{the}\:{equation}\:{to}\:{two} \\ $$$${circles}\:{which}\:{touch}\:{the}\: \\ $$$${x}−{axis}\:{at}\:{the}\:{origin} \\ $$$${and}\:{also}\:{touch}\:{the}\:{line} \\ $$$$\mathrm{12}{x}+\mathrm{5}{y}=\mathrm{60} \\ $$

Question Number 54268    Answers: 0   Comments: 1

Question Number 54259    Answers: 1   Comments: 1

Question Number 54258    Answers: 0   Comments: 1

Question Number 54273    Answers: 2   Comments: 0

Question Number 54248    Answers: 2   Comments: 1

Question Number 54242    Answers: 2   Comments: 0

Question Number 54240    Answers: 1   Comments: 1

Question Number 54239    Answers: 1   Comments: 0

Question Number 54229    Answers: 1   Comments: 1

Question Number 54226    Answers: 0   Comments: 4

Question Number 54224    Answers: 2   Comments: 4

∫_0 ^( (π/4)) ((sinx+cosx)/(16+9sin2x)) dx =?

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{16}+\mathrm{9sin2}{x}}\:{dx}\:=? \\ $$

Question Number 54219    Answers: 1   Comments: 0

tan^6 (π/9)−33 tan^4 (π/9)+27tan^2 (π/9) =

$$\mathrm{tan}^{\mathrm{6}} \:\frac{\pi}{\mathrm{9}}−\mathrm{33}\:\mathrm{tan}^{\mathrm{4}} \frac{\pi}{\mathrm{9}}+\mathrm{27tan}^{\mathrm{2}} \:\frac{\pi}{\mathrm{9}}\:=\: \\ $$

Question Number 54209    Answers: 2   Comments: 0

Question Number 54206    Answers: 1   Comments: 2

Question Number 54194    Answers: 1   Comments: 1

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