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Maths-

General

Easy

Question

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 $theta$ ,

$1 \leq A \leq 2$
$3 / 4 \leq A \leq 1$
$13 / 16 \leq A \leq 1$
$3 / 4 \leq A \leq 13 / 16$

The correct answer is: $3 divided by 4 less or equal than A less or equal than 1$

We have $sin to the power of 2 end exponent invisible function application theta plus cos to the power of 4 end exponent invisible function application theta equals sin to the power of 2 end exponent invisible function application theta plus cos to the power of 2 end exponent invisible function application cos to the power of 2 end exponent invisible function application theta less or equal than sin to the power of 2 end exponent invisible function application theta plus cos to the power of 2 end exponent invisible function application blank theta left square bracket because cos to the power of 2 end exponent invisible function application theta less or equal than 1 right square bracket$
Again, $A equals sin to the power of 2 end exponent invisible function application theta plus cos to the power of 4 end exponent invisible function application theta equals 1 minus cos to the power of 2 end exponent invisible function application theta plus cos to the power of 4 end exponent invisible function application theta equals 1 plus left parenthesis cos to the power of 4 end exponent invisible function application theta minus cos to the power of 2 end exponent invisible function application theta right parenthesis$
$equals 1 plus open parentheses cos to the power of 2 end exponent invisible function application theta minus fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 2 end exponent minus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 3 over denominator 4 end fraction plus open parentheses cos to the power of 2 end exponent invisible function application theta minus fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 2 end exponent greater or equal than fraction numerator 3 over denominator 4 end fraction$
Hence, $3 divided by 4 less or equal than A less or equal than 1$

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