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Question

$I f blank A$ and $blank B$ are acute positive angles satisfying the equations $3 sin to the power of 2 end exponent invisible function application A plus 2 sin to the power of 2 end exponent invisible function application B equals 1$ and $blank 3 sin invisible function application 2 A minus 2 sin invisible function application 2 B equals 0 comma$ then $A plus 2 blank B$ is equal to

$π$
$\frac{π}{2}$
$\frac{π}{4}$
$\frac{π}{6}$

The correct answer is: $fraction numerator pi over denominator 2 end fraction$

$3 sin to the power of 2 end exponent invisible function application A plus 2 sin to the power of 2 end exponent invisible function application B equals 1$
$rightwards double arrow 3 sin to the power of 2 end exponent invisible function application A equals cos invisible function application 2 B$
Also $3 sin invisible function application 2 A minus 2 sin invisible function application 2 B equals 0$
$rightwards double arrow sin invisible function application 2 B equals fraction numerator 3 over denominator 2 end fraction sin invisible function application 2 A$
Now $comma cos invisible function application open parentheses A plus 2 B close parentheses equals cos invisible function application A cos invisible function application 2 B minus sin invisible function application A sin invisible function application 2 B equals cos invisible function application A 3 sin to the power of 2 end exponent invisible function application A minus sin invisible function application A fraction numerator 3 over denominator 2 end fraction sin invisible function application 2 A$
$equals 3 sin to the power of 2 end exponent invisible function application A cos invisible function application A minus 3 sin to the power of 2 end exponent invisible function application A cos invisible function application A equals 0$
$therefore A plus 2 B equals pi divided by 2$

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parallel

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parallel

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If $log subscript 10 end subscript invisible function application open square brackets fraction numerator 1 over denominator 2 to the power of x end exponent plus blank x minus 1 end fraction close square brackets equals x open square brackets log subscript 10 end subscript invisible function application 5 minus 1 close square brackets comma blank t h e n blank x equals$

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parallel

any $increment A B C comma$ the value of $a open parentheses b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses cos invisible function application A plus b left parenthesis c to the power of 2 end exponent plus a to the power of 2 end exponent right parenthesis cos invisible function application B plus c left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent right parenthesis cos invisible function application C equals$

any $increment A B C comma$ the value of $a open parentheses b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses cos invisible function application A plus b left parenthesis c to the power of 2 end exponent plus a to the power of 2 end exponent right parenthesis cos invisible function application B plus c left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent right parenthesis cos invisible function application C equals$

$fraction numerator sin invisible function application x over denominator sin invisible function application y end fraction equals fraction numerator 1 over denominator 2 end fraction comma fraction numerator cos invisible function application x over denominator cos invisible function application y end fraction equals fraction numerator 3 over denominator 2 end fraction blank w h e r e blank x comma blank y blank element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses comma blank t h e n blank t h e blank v a l u e blank o f blank left parenthesis x plus y right parenthesis blank i s blank e q u a l blank t o$

$fraction numerator sin invisible function application x over denominator sin invisible function application y end fraction equals fraction numerator 1 over denominator 2 end fraction comma fraction numerator cos invisible function application x over denominator cos invisible function application y end fraction equals fraction numerator 3 over denominator 2 end fraction blank w h e r e blank x comma blank y blank element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses comma blank t h e n blank t h e blank v a l u e blank o f blank left parenthesis x plus y right parenthesis blank i s blank e q u a l blank t o$

$tan invisible function application 3 theta plus tan invisible function application theta equals 2 tan invisible function application 2 theta$ , then $blank theta$ is equal to $open parentheses n element of Z close parentheses$

$tan invisible function application 3 theta plus tan invisible function application theta equals 2 tan invisible function application 2 theta$ , then $blank theta$ is equal to $open parentheses n element of Z close parentheses$

parallel

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