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Find the extreme values of the follo...

Find the extreme values of the following function over R.
`(i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x)`
`(ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3`
`(iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x`
`(v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x) `

A

3

B

2

C

`sqrt(3)`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-PERIODICITY AND EXTREME VALUES-Practice Sheet (Exericise-I) Level-II (Straight Objective Type Questions)
  1. sin theta sin (60^(@) - theta) sin (60^(@)+ theta) in [-k,k] rArr k=

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  2. The minimum and maximum values of sin^(2) (60^(@)-x) + sin^(2) ( 60^(@...

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  3. Find the extreme values of the following function over R. (i)...

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  4. The extreme values of 4cos(x^(2)).cos((pi)/(3)+x^(2)).cos((pi)/(3)-x^...

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  5. (sin x + cos x)^(2) + cos^(2)((pi)/(4) + x) in

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  6. For all values of theta, the values of 3-cos theta+cos (theta+(pi)/(3)...

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  7. 5 cos theta + 3 cos ( theta - (pi)/(3) )+8 in

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  8. A+B = 90^(@) rArr cos A cos B in

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  9. A+B = 90^(@) rArr sin A + sin Bin

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  10. The range of cos^(2) x + sin^(4) x is

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  11. The range of f(x)=-3 cos sqrt(3x+x+x^(2)) is

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  12. The minimum and maximum values of 8 cos 3x - 15 sin3x are

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  13. The maximum value of (3 ) /( 5 sin x-12 cos x+19) is

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  14. cos5x=16 cos^(5) x -20 cos^(3) x +5 cos x in

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  15. 3 sin^(2) x -4 cos^(2) x in

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  16. The maximum value of cos x ((cos x )/( 1- sin x) + (1- sin x)/( cos x)...

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  17. Minimum value of 9 sec^(2) theta + 4 cosec^(2) theta + 7 is

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  18. The minimum value of the expression sin alpha + sin beta+sin lambda, w...

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  19. If a le 3 cos x + 5 sin ( x - pi//6) le b for all x , then ( a, b) is

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  20. cos^(2) (60^(@) - x) + cos^(2) (60^(@) +x) in

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