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Maths-

General

Easy

Question

$I f blank x element of open parentheses pi comma fraction numerator 3 pi over denominator 2 end fraction close parentheses comma blank t h e n blank 4 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator pi over denominator 4 end fraction minus fraction numerator x over denominator 2 end fraction close parentheses plus square root of 4 sin to the power of 4 end exponent invisible function application x plus sin to the power of 2 end exponent invisible function application 2 x end root$ is always equal to

1/3
2
3
None of these

The correct answer is: 2

Area of triangle $blank A R Q equals fraction numerator b over denominator open parentheses k plus 1 close parentheses end fraction cross times fraction numerator k c over denominator open parentheses K plus 1 close parentheses end fraction cross times fraction numerator 1 over denominator 2 end fraction sin invisible function application A equals fraction numerator k increment over denominator open parentheses k plus 1 close parentheses to the power of 2 end exponent end fraction$
Similarly, area $blank open parentheses increment B P R close parentheses equals open parentheses increment P C Q close parentheses equals fraction numerator k increment over denominator open parentheses k plus 1 close parentheses to the power of 2 end exponent end fraction$
Now $comma fraction numerator increment P Q R over denominator increment A B C end fraction equals fraction numerator 1 over denominator 3 end fraction$
$rightwards double arrow fraction numerator increment minus fraction numerator 3 k over denominator open parentheses k plus 1 close parentheses to the power of 2 end exponent end fraction increment over denominator increment end fraction equals fraction numerator 1 over denominator 3 end fraction$
$rightwards double arrow 2 k to the power of 2 end exponent minus 5 k plus 2 equals 0$
$rightwards double arrow k equals fraction numerator 1 over denominator 2 end fraction comma blank 2$
$equals 2 open parentheses 1 plus cos invisible function application open parentheses fraction numerator pi over denominator 2 end fraction minus x close parentheses close parentheses plus 2 open vertical bar sin invisible function application x close vertical bar equals 2 plus 2 sin invisible function application x minus 2 sin invisible function application x blank a s blank x element of open parentheses pi comma fraction numerator 3 pi over denominator 2 end fraction close parentheses equals 2 blank$

Related Questions to study

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

$I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ 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

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

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

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