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AllQuestion and Answers: Page 353

Question Number 177975 Answers: 1 Comments: 0

Question Number 177964 Answers: 3 Comments: 1

(1/(sec15 sin15 cos30))=?

$$\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$

Question Number 177957 Answers: 2 Comments: 0

let a > 0 find the sum of the infinite series 1 + (((loga)^2 )/(2!)) + (((loga)^4 )/(4!)) + (((loga)^6 )/(6!))...

$$\mathrm{let}\:\:\mathrm{a}\:>\:\mathrm{0}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{infinite}\: \\ $$$$\mathrm{series} \\ $$$$\:\mathrm{1}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{2}} \:}{\mathrm{2}!}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{4}} \:}{\mathrm{4}!}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{6}} \:}{\mathrm{6}!}... \\ $$

Question Number 177933 Answers: 2 Comments: 0

If 1+sin x+sin^2 x+sin^3 x+...∞ =4+2(√3) ,0<x<π Find the value of x

$$\mathrm{If}\:\mathrm{1}+\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+...\infty \\ $$$$=\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}\:\:,\mathrm{0}<\mathrm{x}<\pi\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 177932 Answers: 1 Comments: 0

If a,b,c are in A.P show that (1/( (√b)+(√c))),(1/( (√c) +(√a))),(1/( (√b)+(√a))),are in A.P

$$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{c}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{c}}\:+\sqrt{\mathrm{a}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{a}}},\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P} \\ $$

Question Number 177931 Answers: 1 Comments: 0

Prove by the principle of induction that 1.4.7+2.5.8+3.6.9+...n(n+3)(n+6) =(n/4)(n+1)(n+6)(n+7)

$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{the}\:\mathrm{principle}\:\mathrm{of}\: \\ $$$$\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}.\mathrm{4}.\mathrm{7}+\mathrm{2}.\mathrm{5}.\mathrm{8}+\mathrm{3}.\mathrm{6}.\mathrm{9}+...\mathrm{n}\left(\mathrm{n}+\mathrm{3}\right)\left(\mathrm{n}+\mathrm{6}\right) \\ $$$$=\frac{\mathrm{n}}{\mathrm{4}}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{6}\right)\left(\mathrm{n}+\mathrm{7}\right) \\ $$

Question Number 177930 Answers: 2 Comments: 0

Find the LCM 14a^2 b^3 c^4 ,20ab^4 c^4 and 35a^5 b^3 c

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{LCM}\: \\ $$$$\mathrm{14a}^{\mathrm{2}} \mathrm{b}^{\mathrm{3}} \mathrm{c}^{\mathrm{4}} ,\mathrm{20ab}^{\mathrm{4}} \mathrm{c}^{\mathrm{4}} \:\mathrm{and} \\ $$$$\:\mathrm{35a}^{\mathrm{5}} \mathrm{b}^{\mathrm{3}} \mathrm{c} \\ $$

Question Number 177929 Answers: 1 Comments: 0

Find LCM 3y+12,y^2 −16 and y^4 −64y

$$\mathrm{Find}\:\mathrm{LCM}\: \\ $$$$\mathrm{3y}+\mathrm{12},\mathrm{y}^{\mathrm{2}} −\mathrm{16}\:\mathrm{and}\:\mathrm{y}^{\mathrm{4}} −\mathrm{64y} \\ $$

Question Number 177928 Answers: 1 Comments: 0

Prove that [((x^3 +y^3 )/((x−y)^2 +3y))]÷[(((x+y)^2 −3xy)/(x^3 −y^3 ))]×[((xy)/(x^2 −y^2 ))]=xy

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\left[\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}} +\mathrm{3y}}\right]\boldsymbol{\div}\left[\frac{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} −\mathrm{3xy}}{\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}} }\right]×\left[\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }\right]=\mathrm{xy} \\ $$

Question Number 177922 Answers: 1 Comments: 0

Question Number 177913 Answers: 0 Comments: 0

if I_n =∫xsin^n x dx and I_n = −((xsin^(n−1) x cosx )/n) +((sin^n x )/n^2 )+f(n)I_(n−2) then f(n) = ?

$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{if}}\:\:\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} =\int\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:\:\:\boldsymbol{\mathrm{and}}\:\: \\ $$$$\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} \:=\:−\frac{\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{cosx}}\:}{\boldsymbol{\mathrm{n}}}\:+\frac{\boldsymbol{\mathrm{sin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+\mathrm{f}\left(\mathrm{n}\right)\mathrm{I}_{\mathrm{n}−\mathrm{2}} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{f}\left(\mathrm{n}\right)\:=\:? \\ $$

Question Number 177914 Answers: 2 Comments: 0

(1) ((2sin26+2cos64)/(4sin13 cos13))=? (2) (1/(sec15 sin15 cos30))=?

$$\left(\mathrm{1}\right)\:\:\:\:\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{4}{sin}\mathrm{13}\:{cos}\mathrm{13}}=? \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$

Question Number 177910 Answers: 2 Comments: 0

Question Number 177906 Answers: 1 Comments: 0

∫_0 ^1 ((sin x(cos^2 x−cos^2 (π/5))(cos^2 x−cos^2 ((2π)/5)))/(sin 5x)) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{5}}\right)\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{5}}\right)}{\mathrm{sin}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$

Question Number 177900 Answers: 1 Comments: 0

Question Number 177890 Answers: 0 Comments: 2

Question Number 177886 Answers: 1 Comments: 1

Question Number 177884 Answers: 1 Comments: 0

Question Number 177880 Answers: 1 Comments: 0

Question Number 177875 Answers: 0 Comments: 1

Question Number 177873 Answers: 2 Comments: 0

solve for x∈R (√(3+(√(3+(√(3+(√(3+(√(3+x))))))))))=x

$${solve}\:{for}\:{x}\in\mathbb{R} \\ $$$$\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+{x}}}}}}={x} \\ $$

Question Number 177870 Answers: 0 Comments: 0

Question Number 177867 Answers: 1 Comments: 0

Question Number 177866 Answers: 2 Comments: 0

Question Number 177865 Answers: 2 Comments: 0

Question Number 177859 Answers: 1 Comments: 0

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