Home
Class 12
MATHS
Find the maximum and minimum values of c...

Find the maximum and minimum values of `cos^2theta-6s inthetacostheta+3sin^2theta+2.`

Text Solution

Verified by Experts

`cos^(2)theta-6sintheta cos theta+3sin^(2)theta+2`
`=(1+cos 2 theta)/(2)-3sin2 theta+((1-cos 2 theta))/(2)+2`
`=4-cos 2 theta-3 sin 2 theta`
Now, `-cos 2 theta-3sin 2 theta in [-sqrt(10),sqrt(10)]`
`rArr 4-cos 2 theta-3 sin 2 theta in[4-sqrt(10),4+sqrt(10))`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Solved example|15 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Find the maximum and minimum values of cos^2theta-6sinthetacostheta+3sin^2theta+2.

Find the maximum and minimum value of cos^(2) theta- 6 sin theta cos theta + 3 sin^(2) theta + 2 .

Maximum and minimum value of 2sin^(2)theta-3sintheta+2 is-

Find the maximum and minimum values of the expression: a cos theta + b sin theta

If M and m denotes maximum and minimum value of sqrt(49cos^2theta + sin^2theta) + sqrt(49sin^2theta+cos^2theta then find the value of (M+m) is

Find the maximum and minimum value of 5cos theta+3sin(theta+(pi)/(6)) for all real values of theta . .

Solve : 3-2 cos theta -4 sin theta - cos 2theta+sin 2theta=0 .

Find the maximum and minimum values of the following expressions (i) a cos theta - bsin theta (ii) 7 cos theta + 24 sin theta

The maximum value of the expression 1/(sin^2theta+3sinthetacostheta+5cos^2theta)

Find maximum and minimum values of 2sin(theta+(pi)/(6))+sqrt(3)cos(theta-(pi)/(6))