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Assertion (A ) : The maximum value of 2...

Assertion (A ) : The maximum value of `2 cos^(2) theta + sqrt(5) cos theta sin theta + 4 sin^(2) theta ` is `(9)/(2)`
Reason (R ) : The maximum value of `acos^(2) theta + b cos theta sin theta + c sin^(2) theta ` is`(1)/(2) [ (a+c) + sqrt((a-c)^(2) + b^(2))]`

A

A is true , R is true and R is correct explanation of A

B

A is true , R is true and R is not correct explanation of A

C

A is true , R is false

D

A is false , R is true

Text Solution

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The correct Answer is:
A
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The maximum value of the expression (1)/( sin^(2) theta + 3 sin theta cos theta + 5cos^(2) theta) is

4 sin 5 theta cos 3 theta sin 2 theta

Knowledge Check

  • The minimum value of 4 cos theta + 2sqrt(3) sin theta is

    A
    `-2sqrt(7)`
    B
    `-3sqrt(7)`
    C
    `3sqrt(7) `
    D
    `2sqrt(7) `

  • The least value of cos^(2) theta - 6 sin theta.cos theta+ 3 sin^(2) theta+2 is

    A
    `4+ sqrt( 10)`
    B
    `4- sqrt( 10)`
    C
    `0`
    D
    `4`

  • The maximum value of sin^(2) theta + cos^4 theta is

    A
    0
    B
    `1`
    C
    `3//4`
    D
    `pi//2 `

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    If cos theta + sqrt(3) sin theta = 2 then theta =

    If sqrt(3) cos theta + sin theta = sqrt(2) , then theta =

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