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Question

$I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are two distinct roots of the equation $a cos invisible function application x plus b sin invisible function application x equals c comma blank t h e n tan invisible function application fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction$ is equal to

$\frac{a}{b}$
$\frac{b}{a}$
$\frac{c}{a}$
$\frac{a}{c}$

The correct answer is: $fraction numerator b over denominator a end fraction$

$a cos invisible function application x plus b sin invisible function application x equals c$
$rightwards double arrow fraction numerator a open parentheses 1 minus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction close parentheses over denominator 1 plus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction end fraction plus fraction numerator 2 b tan invisible function application fraction numerator x over denominator 2 end fraction over denominator 1 plus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction end fraction equals c$
$rightwards double arrow open parentheses c plus a close parentheses tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction minus 2 b tan invisible function application fraction numerator x over denominator 2 end fraction plus c minus a equals 0$
$rightwards double arrow tan invisible function application fraction numerator x subscript 1 end subscript over denominator 2 end fraction plus tan invisible function application fraction numerator x subscript 2 end subscript over denominator 2 end fraction equals fraction numerator 2 b over denominator c plus a end fraction a n d tan invisible function application fraction numerator x subscript 1 end subscript over denominator 2 end fraction tan invisible function application fraction numerator x subscript 2 end subscript over denominator 2 end fraction equals fraction numerator c minus a over denominator c plus a end fraction$
$rightwards double arrow tan invisible function application open parentheses fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction close parentheses equals fraction numerator fraction numerator 2 b over denominator c plus a end fraction over denominator 1 minus fraction numerator c minus a over denominator c plus a end fraction end fraction equals fraction numerator 2 b over denominator 2 a end fraction equals fraction numerator b over denominator a end fraction$

Related Questions to study

$I f fraction numerator sin invisible function application open parentheses x plus y close parentheses over denominator sin invisible function application open parentheses x minus y close parentheses end fraction equals fraction numerator a plus b over denominator a minus b end fraction comma blank t h e n fraction numerator tan invisible function application x over denominator tan invisible function application y end fraction blank i s blank e q u a l blank t o$

$I f fraction numerator sin invisible function application open parentheses x plus y close parentheses over denominator sin invisible function application open parentheses x minus y close parentheses end fraction equals fraction numerator a plus b over denominator a minus b end fraction comma blank t h e n fraction numerator tan invisible function application x over denominator tan invisible function application y end fraction blank i s blank e q u a l blank t o$

Which of the following is not the general solution of $2 to the power of cos invisible function application 2 x end exponent plus 1 equals 3.2 to the power of negative sin to the power of 2 end exponent invisible function application x end exponent ?$

Which of the following is not the general solution of $2 to the power of cos invisible function application 2 x end exponent plus 1 equals 3.2 to the power of negative sin to the power of 2 end exponent invisible function application x end exponent ?$

In triangle $A B C comma$ base $B C$ and area of triangle $increment$ are fixed. Locus of the centroid of triangle $A B C$ is a straight line that is

In triangle $A B C comma$ base $B C$ and area of triangle $increment$ are fixed. Locus of the centroid of triangle $A B C$ is a straight line that is

parallel

The radii $r subscript 1 end subscript comma blank r subscript 2 end subscript comma blank r subscript 3 end subscript$ of the escribed circles of the triangle $A B C$ are in H.P. If the area of the triangle is 24 $c m to the power of 2 end exponent$ and its perimeter is 24 cm, then the length of its largest side is

The radii $r subscript 1 end subscript comma blank r subscript 2 end subscript comma blank r subscript 3 end subscript$ of the escribed circles of the triangle $A B C$ are in H.P. If the area of the triangle is 24 $c m to the power of 2 end exponent$ and its perimeter is 24 cm, then the length of its largest side is

In an acute angled triangle $A B C comma blank r plus r subscript 1 end subscript equals r subscript 2 end subscript plus r subscript 3 end subscript blank$ and $blank angle B greater than fraction numerator pi over denominator 3 end fraction comma$ then

In an acute angled triangle $A B C comma blank r plus r subscript 1 end subscript equals r subscript 2 end subscript plus r subscript 3 end subscript blank$ and $blank angle B greater than fraction numerator pi over denominator 3 end fraction comma$ then

If $´ O ´$ is the circumcentre of $increment A B C blank$ and $blank R subscript 1 end subscript comma R subscript 2 end subscript blank$ and $blank R subscript 3 end subscript$ are the radii of the circumcircles of triangles $O B C comma blank O C A blank$ and $blank O A B comma$ respectively, then $fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction$ has the value equal to

If $´ O ´$ is the circumcentre of $increment A B C blank$ and $blank R subscript 1 end subscript comma R subscript 2 end subscript blank$ and $blank R subscript 3 end subscript$ are the radii of the circumcircles of triangles $O B C comma blank O C A blank$ and $blank O A B comma$ respectively, then $fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction$ has the value equal to

parallel

In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is $4 A$ , then that in the secondary is

In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is $4 A$ , then that in the secondary is

Physics-General

A transformer is often filled with oil. The oil used should have

A transformer is often filled with oil. The oil used should have

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The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first

The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first
Physics-General

parallel

A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e =200sin 100 $pi t$ . The magnetic induction is

A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e =200sin 100 $pi t$ . The magnetic induction is

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Quantity that remains unchanged in a transformer is

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Two parallel rails of a railways track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is one metre. A train is travelling with a velocity of 72 km- $h to the power of negative 1 end exponent$ along the track. The reading of the millivotmeter (in mV) is : (Vertical component of the earth’s magnetic induction is $blank 2 cross times 10 to the power of negative 5 end exponent T right parenthesis$

Two parallel rails of a railways track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is one metre. A train is travelling with a velocity of 72 km- $h to the power of negative 1 end exponent$ along the track. The reading of the millivotmeter (in mV) is : (Vertical component of the earth’s magnetic induction is $blank 2 cross times 10 to the power of negative 5 end exponent T right parenthesis$

Physics-General

parallel

A circular coil of diameter 21 cm is placed in a magnetic field of induction 10^-4 T. the magnitude of flux linked with coil when the plane of coil makes an angle 30 $degree$ with the field is

A circular coil of diameter 21 cm is placed in a magnetic field of induction 10^-4 T. the magnitude of flux linked with coil when the plane of coil makes an angle 30 $degree$ with the field is

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A 50 turns circular coil has a radius of 3 cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field $B$ increased from 0.10 to 0.35 T in 2 millisecond. The average induced emf in the coil is

A 50 turns circular coil has a radius of 3 cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field $B$ increased from 0.10 to 0.35 T in 2 millisecond. The average induced emf in the coil is

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A $50 blank v o l t$ potential difference is suddenly applied to a coil with $L equals 5 cross times 10 to the power of negative 3 end exponent h e n r y$ and $R equals 180 blank o h m$ . The rate of increase of current after $0.001 blank s e c o n d$ is

A $50 blank v o l t$ potential difference is suddenly applied to a coil with $L equals 5 cross times 10 to the power of negative 3 end exponent h e n r y$ and $R equals 180 blank o h m$ . The rate of increase of current after $0.001 blank s e c o n d$ is

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parallel

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