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Question

The side of triangle $A B C$ are in A.P. (order being $a comma blank b comma blank c$ ) and satisfy $fraction numerator 2 factorial over denominator 1 factorial 9 factorial end fraction plus fraction numerator 2 factorial over denominator 3 factorial 7 factorial end fraction plus fraction numerator 1 over denominator 5 factorial 5 factorial end fraction equals fraction numerator 8 to the power of a end exponent over denominator open parentheses 2 b close parentheses factorial blank end fraction comma blank$ then the value of $cos invisible function application A plus cos invisible function application B$ is

$\frac{12}{7}$
$\frac{13}{7}$
$\frac{11}{7}$
$\frac{10}{7}$

The correct answer is: $fraction numerator 12 over denominator 7 end fraction$

$fraction numerator 2 factorial over denominator 1 factorial 9 factorial end fraction plus fraction numerator 2 over denominator 3 factorial 7 factorial end fraction plus fraction numerator 1 over denominator 5 factorial 5 factorial end fraction equals fraction numerator 2 over denominator 10 factorial end fraction open parentheses blank to the power of 10 end exponent C subscript 1 end subscript close parentheses plus fraction numerator 2 over denominator 10 factorial end fraction open parentheses blank to the power of 10 end exponent C subscript 3 end subscript close parentheses plus fraction numerator 1 over denominator 10 factorial end fraction blank to the power of 10 end exponent C subscript 5 end subscript equals fraction numerator 1 over denominator 10 factorial end fraction open parentheses blank to the power of 10 end exponent C subscript 1 end subscript plus blank to the power of 10 end exponent C subscript 9 end subscript plus blank to the power of 10 end exponent C subscript 3 end subscript plus blank to the power of 10 end exponent C subscript 7 end subscript plus blank to the power of 10 end exponent C subscript 5 end subscript close parentheses$
$equals fraction numerator 1 over denominator 10 factorial end fraction open parentheses 2 to the power of 10 minus 1 end exponent close parentheses equals fraction numerator 2 to the power of 9 end exponent over denominator 10 factorial end fraction equals fraction numerator 8 to the power of a end exponent over denominator open parentheses 2 b close parentheses factorial end fraction blank open parentheses g i v e n close parentheses$ $rightwards double arrow 3 a equals 9 comma blank 2 b equals 10 blank rightwards double arrow a equals 3 comma blank b equals 5$
Also, $blank a comma blank b comma blank c blank$ are in A.P $. blank rightwards double arrow c equals 7$
$cos invisible function application A equals fraction numerator b to the power of 2 end exponent plus c to the power of 2 end exponent minus a to the power of 2 end exponent over denominator 2 b c end fraction equals fraction numerator 25 plus 49 minus 9 over denominator 2 cross times 5 cross times 7 end fraction equals fraction numerator 65 over denominator 2 cross times 5 cross times 7 end fraction equals fraction numerator 13 over denominator 14 end fraction$
$cos invisible function application B equals fraction numerator a to the power of 2 end exponent plus c to the power of 2 end exponent minus b to the power of 2 end exponent over denominator 2 a c end fraction equals fraction numerator 9 plus 49 minus 25 over denominator 2 cross times 3 cross times 7 end fraction equals fraction numerator 11 over denominator 14 end fraction$
$rightwards double arrow cos invisible function application A plus cos invisible function application B equals fraction numerator 13 plus 11 over denominator 14 end fraction equals fraction numerator 24 over denominator 14 end fraction equals fraction numerator 12 over denominator 7 end fraction$

Related Questions to study

One of the general solutions of $4 sin invisible function application theta sin invisible function application 2 theta sin invisible function application 4 theta equals sin invisible function application 3 theta$ is

One of the general solutions of $4 sin invisible function application theta sin invisible function application 2 theta sin invisible function application 4 theta equals sin invisible function application 3 theta$ is

Which of the following is correct?

Which of the following is correct?

The number of solutions of $sec to the power of 2 end exponent invisible function application theta plus c o s e c to the power of 2 end exponent theta plus 2 blank c o s e c to the power of 2 end exponent theta equals 8 comma blank 0 less or equal than theta less or equal than pi divided by 2$ is

The number of solutions of $sec to the power of 2 end exponent invisible function application theta plus c o s e c to the power of 2 end exponent theta plus 2 blank c o s e c to the power of 2 end exponent theta equals 8 comma blank 0 less or equal than theta less or equal than pi divided by 2$ is

parallel

$I f sin invisible function application 2 theta equals cos invisible function application 3 theta blank a n d blank theta$ is an acute angle, then $sin invisible function application theta$ equals

$I f sin invisible function application 2 theta equals cos invisible function application 3 theta blank a n d blank theta$ is an acute angle, then $sin invisible function application theta$ equals

If $cos invisible function application B cos invisible function application C plus sin invisible function application B sin invisible function application C sin to the power of 2 end exponent invisible function application A equals 1 comma$ then triangle $A B C$ is

If $cos invisible function application B cos invisible function application C plus sin invisible function application B sin invisible function application C sin to the power of 2 end exponent invisible function application A equals 1 comma$ then triangle $A B C$ is

The number of values of $theta$ which satisfy the equation $sin invisible function application 3 theta minus sin invisible function application theta equals 4 cos to the power of 2 end exponent invisible function application theta minus 2 comma blank for all blank theta element of open square brackets 0 comma blank 2 pi close square brackets comma$ is

The number of values of $theta$ which satisfy the equation $sin invisible function application 3 theta minus sin invisible function application theta equals 4 cos to the power of 2 end exponent invisible function application theta minus 2 comma blank for all blank theta element of open square brackets 0 comma blank 2 pi close square brackets comma$ is

parallel

The general solution of the trigonometric equation $sin invisible function application x plus cos invisible function application x equals 1$ is given by

The general solution of the trigonometric equation $sin invisible function application x plus cos invisible function application x equals 1$ is given by

12 guests at a dinner party are to be seated along a circular table. Supposing that the master and mistress of the house have fixed seats opposite one another, and that there are two specified guests who must always, be placed next to one another, the number of ways in which the company can be placed, is-

12 guests at a dinner party are to be seated along a circular table. Supposing that the master and mistress of the house have fixed seats opposite one another, and that there are two specified guests who must always, be placed next to one another, the number of ways in which the company can be placed, is-

In a conference 10 speakers are present. If S₁ wants to speak before S₂ and S₂ wants to speak after S₃, then the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number is-

In a conference 10 speakers are present. If S₁ wants to speak before S₂ and S₂ wants to speak after S₃, then the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number is-

parallel

The streets of a city are arranged like the lines of a chess board. There are m streets running North to South & 'n' streets running East to West. The number of ways in which a man can travel from NW to SE corner going the shortest possible distance is-

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The number of permutations which can be formed out of the letters of the word 'SERIES' taking three letters together is-

The number of ways in which 10 different balls can be placed in three different boxes so that at least one box remains empty

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parallel

The number of ways in which 5 different balls can be placed in three different boxes so that no box remains empty -

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In a hall there are 10 bulbs and their 10 buttons. In how many ways this hall can be enlightened?

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parallel

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