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Prove that: |sintheta"sin"(60-theta)sin(...

Prove that: `|sintheta"sin"(60-theta)sin(60+theta)|lt=1/4` for all values of `theta` .

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To prove that \( | \sin \theta \cdot \sin(60^\circ - \theta) \cdot \sin(60^\circ + \theta) | \leq \frac{1}{4} \) for all values of \( \theta \), we can follow these steps: ### Step 1: Rewrite the expression We start with the expression: \[ | \sin \theta \cdot \sin(60^\circ - \theta) \cdot \sin(60^\circ + \theta) | \] ...
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Knowledge Check

  • If A=sin^(2) theta+cos^(4) theta , then for all values of theta

    A
    ` 1 le A le 2`
    B
    `3//4 le A le 1`
    C
    `13//16 le A le 1`
    D
    `3//4 le A le 13//16`
  • If A= cos^(4)theta+sin^(2)theta , then for all values of theta :

    A
    `1 lt A le2`
    B
    `(13)/(16) le A le 1`
    C
    `(3)/(4) le A le (13)/(16)`
    D
    `(3)/(4) le A le 1`
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