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Maths-

General

Easy

Question

e equation $sin to the power of 2 end exponent invisible function application theta equals fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction$ is possible if

$x = y$
$x = - y$
$2 x = y$
None of these

The correct answer is: $x equals y$

We have $fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction equals fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator x over denominator y end fraction plus fraction numerator y over denominator x end fraction close parentheses$
Now $comma sin to the power of 2 end exponent invisible function application theta equals fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction rightwards double arrow fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction greater or equal than 0 blank open square brackets because sin to the power of 2 end exponent invisible function application theta greater or equal than 0 close square brackets$
Therefore, $x blank a n d blank y$ have the same sign
Now $comma blank fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction equals fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator x over denominator y end fraction plus fraction numerator y over denominator x end fraction close parentheses rightwards double arrow fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction greater or equal than 1 open parentheses because A. M. blank greater or equal than G. M. close parentheses$
But $sin to the power of 2 end exponent invisible function application theta less or equal than 1. blank$ Therefore $comma blank fraction numerator x to the power of 2 end exponent plus y to the power of 2 end exponent over denominator 2 x y end fraction equals 1 rightwards double arrow x equals y$

Related Questions to study

$increment A B C comma sin invisible function application A plus sin invisible function application B plus sin invisible function application C equals 1 plus square root of 2$ and $cos invisible function application A plus cos invisible function application plus cos invisible function application C equals square root of 2$ if the triangle is

$increment A B C comma sin invisible function application A plus sin invisible function application B plus sin invisible function application C equals 1 plus square root of 2$ and $cos invisible function application A plus cos invisible function application plus cos invisible function application C equals square root of 2$ if the triangle is

ven $A equals sin to the power of 2 end exponent invisible function application theta plus cos to the power of 2 end exponent invisible function application theta comma$ then for all real $theta$ ,

ven $A equals sin to the power of 2 end exponent invisible function application theta plus cos to the power of 2 end exponent invisible function application theta comma$ then for all real $theta$ ,

$open parentheses 1 plus tan invisible function application alpha close parentheses open parentheses 1 plus tan invisible function application 4 alpha close parentheses equals 2 comma blank alpha element of open parentheses 0 comma blank pi divided by 16 close parentheses$ then $alpha$ is equal to

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parallel

Let $f open parentheses theta close parentheses equals sin invisible function application theta left parenthesis sin invisible function application theta plus sin invisible function application 3 theta right parenthesis.$ Then $f left parenthesis theta right parenthesis$ is

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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

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Hydrogen burns in air with a

Hydrogen burns in air with a

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Metal hydride on treatment with water gives

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parallel

Which is used hydrogen generators

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

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Chemistry-General

Assertion :Outermost electronic configuration of most electropositive elements is ns² np³.
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Physics-General

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Physics-General

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Physics-General

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Physics-General

parallel

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