If $\;A = {\sin ^2}{\rm{\theta }} + {\cos ^4}{\rm{\theta }}$ then for all real values of ${\rm{\theta }}$

$\frac{{13}}{{16}} \le A \le 1$

$\frac{3}{4} \le A \le \frac{{13}}{{16}}$

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Analyzing +4 | -1

\;A = {\sin ^2}\mathrm{\theta } + {\cos ^4}\mathrm{\theta }

then for all real values of

\mathrm{\theta }

View answer and explanation

Correct option: B

\frac{3}{4} \le A \le 1

Option B (

\frac{3}{4} \le A \le 1

) is correct because the minimum value of

A

\frac{3}{4}

and the maximum value is 1, which can be found by completing the square and using trigonometric properties.