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Pooja Sahu

· started a discussion

· 1 Months ago

pp (Question: 207189.0 )

please explain it...

Question:
Find the maximum value of 2cos2\(\theta\) +3sin2\(\theta\)
Options:
A) 0
B) 1
C) 2
D) 3
Solution:
Ans: (d) Maximum value of 2 cos2\(\theta\) + 3 sin2\(\theta\) = 3


2 cos2 + 3 sin2 

   = 2 cos2 + 2 sin2 + sin2 

   = 2(cos2 + sin2) + sin2 

    = 2+ sin2 

Maximum value of sin2 is 1

   = 2+1=3

Knowledge Expert

· commented

· 1 Months ago

Dear Student,

First of all, you must know the trigonometric formula:

When a sin^2x + b cos^2x then

i. If a>b then Max. Value = a and Min. Value = b

ii. If b>a then Max. Value = b and Min. Value = a

Here we have given 3 sin^2x + 2 cos^2x. Since, 3>2, so, Max. Value = 3 and Min. Value = 2

Hope it helps you.
All the Best.
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