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Question Number 57664 Answers: 0 Comments: 1

A luminous point P is inside a circle. A ray emanates from P and after two reflections by the circle,returns to P. If θ be the angle of incidence, a= the distance of P from the centre of the circle and b=the distance of the centre from the point where the ray in its course crosses its diameter through P. prove that tan θ=((a−b)/(a+b))

$${A}\:{luminous}\:{point}\:{P}\:\:{is}\:{inside}\:{a}\:{circle}. \\ $$$${A}\:{ray}\:{emanates}\:{from}\:{P}\:{and}\:{after}\:{two} \\ $$$${reflections}\:{by}\:{the}\:{circle},{returns}\:{to}\:{P}. \\ $$$${If}\:\theta\:{be}\:{the}\:{angle}\:{of}\:{incidence},\:{a}=\:{the} \\ $$$${distance}\:{of}\:{P}\:{from}\:{the}\:{centre}\:{of}\:{the} \\ $$$${circle}\:{and}\:{b}={the}\:{distance}\:{of}\:{the}\:{centre} \\ $$$${from}\:{the}\:{point}\:{where}\:{the}\:{ray}\:{in}\:{its} \\ $$$${course}\:{crosses}\:{its}\:{diameter}\:{through}\:{P}. \\ $$$$ \\ $$$${prove}\:{that}\:\mathrm{tan}\:\theta=\frac{{a}−{b}}{{a}+{b}} \\ $$

Question Number 57653 Answers: 0 Comments: 5

is it possible to find the exact value of I? I=∫_0 ^π sin (sin x) dx

$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:{I}? \\ $$$${I}=\underset{\mathrm{0}} {\overset{\pi} {\int}}\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\:{dx} \\ $$

Question Number 57647 Answers: 0 Comments: 2

find approximate value of ξ(3) by using n−1 ≤n≤n+1 for n integr natural .

$${find}\:\:{approximate}\:{value}\:{of}\:\xi\left(\mathrm{3}\right)\:{by}\:{using}\:\:\:{n}−\mathrm{1}\:\leqslant{n}\leqslant{n}+\mathrm{1}\:\:\:{for}\:{n}\:{integr} \\ $$$${natural}\:. \\ $$

Question Number 57635 Answers: 1 Comments: 2

Find the sum of the cubes of first n even number, and first n odd number.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{even}\:\mathrm{number},\:\:\mathrm{and} \\ $$$$\mathrm{first}\:\mathrm{n}\:\mathrm{odd}\:\mathrm{number}. \\ $$

Question Number 57633 Answers: 1 Comments: 0