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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $B=sin^2 y+cos^4 y$, then for all real y
Solution
Let $B = \sin^{2}y + \cos^{4}y$.Put $t = \cos^{2}y$, so $0 \le t \le 1$.
Then $\sin^{2}y = 1 - t$.
So,
$B = (1 - t) + t^{2} = t^{2} - t + 1$.
Minimum of the quadratic $t^{2} - t + 1$ occurs at
$t = \dfrac{1}{2}$:
$B_{\min} = \dfrac{1}{4} - \dfrac{1}{2} + 1 = \dfrac{3}{4}$.
Maximum occurs at $t = 0$ or $t = 1$:
$B_{\max} = 1$.
Hence,
$B \in \left[\dfrac{3}{4},, 1\right]$.
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