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Maths-

General

Easy

Question

If $blank sin invisible function application x plus cos invisible function application x equals fraction numerator square root of 7 over denominator 2 end fraction blank$ where $blank x element of A comma$ then $tan invisible function application fraction numerator x over denominator 2 end fraction blank$ is equal to

$\frac{3 - \sqrt{7}}{3}$
$\frac{\sqrt{7} - 2}{3}$
$\frac{4 - \sqrt{7}}{4}$
None of these

The correct answer is: $fraction numerator square root of 7 minus 2 over denominator 3 end fraction$

$sin invisible function application x plus cos invisible function application x equals fraction numerator square root of 7 over denominator 2 end fraction blank rightwards double arrow fraction numerator 2 tan invisible function application fraction numerator x over denominator 2 end fraction over denominator open parentheses 1 plus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction close parentheses end fraction plus fraction numerator 1 minus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction over denominator 1 plus tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction end fraction equals fraction numerator square root of 7 over denominator 2 end fraction$
$rightwards double arrow open parentheses square root of 7 plus 2 close parentheses tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction minus 4 tan invisible function application fraction numerator x over denominator 2 end fraction plus open parentheses square root of 7 minus 2 close parentheses equals 0$
$rightwards double arrow tan invisible function application fraction numerator x over denominator 2 end fraction equals fraction numerator 4 plus-or-minus square root of 16 minus 4 open parentheses 7 minus 4 close parentheses end root over denominator 2 open parentheses square root of 7 plus 2 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses square root of 7 plus 2 close parentheses end fraction blank a s fraction numerator x over denominator 2 end fraction less than fraction numerator pi over denominator 8 end fraction$
$equals fraction numerator square root of 7 minus 2 over denominator 3 end fraction$

Related Questions to study

If $fraction numerator 3 pi over denominator 4 end fraction less than alpha less than pi comma blank$ then $square root of 2 cot invisible function application alpha plus fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application alpha end fraction end root blank$ is equal to

If $fraction numerator 3 pi over denominator 4 end fraction less than alpha less than pi comma blank$ then $square root of 2 cot invisible function application alpha plus fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application alpha end fraction end root blank$ is equal to

Hydrogen burns in air with a

Hydrogen burns in air with a

Chemistry-General

Metal hydride on treatment with water gives

Metal hydride on treatment with water gives

Chemistry-General

parallel

Which is used hydrogen generators

Which is used hydrogen generators

Chemistry-General

Assertion:First ionization energy for nitrogen is lower than oxygen.
Reason :Across a period effective nuclear charge decreases.

Assertion:First ionization energy for nitrogen is lower than oxygen.
Reason :Across a period effective nuclear charge decreases.

Chemistry-General

Assertion :Outermost electronic configuration of most electropositive elements is ns² np³.
Reason :ns² np³is stable due to half filled subshell.

Assertion :Outermost electronic configuration of most electropositive elements is ns² np³.
Reason :ns² np³is stable due to half filled subshell.

Physics-General

parallel

Assertion :NO^– ion is isoelectronic with CN^– ion.
Reason :Isoelectronic ions have same number of elelctrons.

Assertion :NO^– ion is isoelectronic with CN^– ion.
Reason :Isoelectronic ions have same number of elelctrons.

Physics-General

Assertion :I.E. of ₇N is more than that of ₈O as well as ₆C.
Reason : This is due to difference in reactivity towards oxygen.

Assertion :I.E. of ₇N is more than that of ₈O as well as ₆C.
Reason : This is due to difference in reactivity towards oxygen.

Physics-General

Assertion :Ground state configuration of Cr is 3d⁵, 4s¹.
Reason : A set of half filled orbitals containing one electron each with their spin parallel provides extra stability to the system.

Assertion :Ground state configuration of Cr is 3d⁵, 4s¹.
Reason : A set of half filled orbitals containing one electron each with their spin parallel provides extra stability to the system.

Physics-General

parallel

Assertion :More is the electron affinity greater is the reducing character.
Reason : Reducing character depends on number of electrons gained.

Assertion :More is the electron affinity greater is the reducing character.
Reason : Reducing character depends on number of electrons gained.

Physics-General

Assertion :Ionization potential across the period is Na < Al < Mg < Si.
Reason : Ionization potential decreases with decrease in atomic size.

Assertion :Ionization potential across the period is Na < Al < Mg < Si.
Reason : Ionization potential decreases with decrease in atomic size.

Physics-General

Assertion :Shielding effect increases as we go down the group.
Reason : More is the number of electrons in the penultimate shell, more is shielding.

Assertion :Shielding effect increases as we go down the group.
Reason : More is the number of electrons in the penultimate shell, more is shielding.

Physics-General

parallel

Assertion :Ionization enthalpy is always negative.
Reason : Energy is always released when electrons are removed.

Assertion :Ionization enthalpy is always negative.
Reason : Energy is always released when electrons are removed.

Physics-General

Assertion :Chemistry of Actinoids is more complicated than Lanthanoids.
Reason : Actinoid elements are radioactive.

Assertion :Chemistry of Actinoids is more complicated than Lanthanoids.
Reason : Actinoid elements are radioactive.

Physics-General

Assertion :Atomic number of the element ununbium is 112.
Reason : Name for digits 1 and 2 is un-and bi-respectively in latin words.

Assertion :Atomic number of the element ununbium is 112.
Reason : Name for digits 1 and 2 is un-and bi-respectively in latin words.

Physics-General

parallel

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