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Q. Find the minimum value of 3cosx + 4sinx + 8.

$${Q}.\:{Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{3}{cosx}\:+\:\mathrm{4}{sinx}\:+\:\mathrm{8}. \\ $$

Question Number 81760 Answers: 0 Comments: 2

prove sin a+sin b+sin c =? 4cos ((a/2))cos ((b/2))cos ((c/2))

$${prove}\: \\ $$$$\mathrm{sin}\:{a}+\mathrm{sin}\:{b}+\mathrm{sin}\:{c}\:=? \\ $$$$\mathrm{4cos}\:\left(\frac{{a}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{b}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{c}}{\mathrm{2}}\right) \\ $$

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Question Number 81739 Answers: 2 Comments: 1

∫(dx/(cos^3 x−sin^3 x))

$$\int\frac{{dx}}{{cos}^{\mathrm{3}} {x}−{sin}^{\mathrm{3}} {x}} \\ $$

Question Number 81734 Answers: 0 Comments: 4

The vertices of quadrilateral lie on the graph of y = lnx and the x−coordinates of these vertices are consecutive positive integer . The area of the quadrilateral is ln (((91)/(90))). what is the x−coordinate of the leftmost vertex

$${The}\:{vertices}\:{of}\:{quadrilateral} \\ $$$${lie}\:{on}\:{the}\:{graph}\:{of}\:{y}\:=\:{lnx}\:{and}\: \\ $$$${the}\:{x}−{coordinates}\:{of}\:{these}\:{vertices} \\ $$$${are}\:{consecutive}\:{positive}\:{integer} \\ $$$$.\:{The}\:{area}\:{of}\:{the}\:{quadrilateral} \\ $$$${is}\:{ln}\:\left(\frac{\mathrm{91}}{\mathrm{90}}\right).\:{what}\:{is}\:{the}\:{x}−{coordinate} \\ $$$${of}\:{the}\:{leftmost}\:{vertex} \\ $$

Question Number 81733 Answers: 0 Comments: 2

Σ_(n=1) ^∞ (n/((n+1)∙5^n )) = ?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}}{\left({n}+\mathrm{1}\right)\centerdot\mathrm{5}^{{n}} }\:\:=\:\:? \\ $$

Question Number 81731 Answers: 0 Comments: 1

If a, b, c are in AP; p, q, r are in HP and ap, bq, cr are in GP, then (p/r)+(r/p) is equal to

$$\mathrm{If}\:\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP};\:\:{p},\:{q},\:{r}\:\mathrm{are}\:\mathrm{in}\:\mathrm{HP}\: \\ $$$$\mathrm{and}\:\:{ap},\:{bq},\:{cr}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP},\:\mathrm{then}\:\frac{{p}}{{r}}+\frac{{r}}{{p}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

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