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Question: Answered & Verified by Expert
Maximum value of 2cos218°-sin18°cosθ+32cosθ+π4+3 is
MathematicsTrigonometric Ratios & IdentitiesTS EAMCETTS EAMCET 2019 (03 May Shift 2)
Options:
  • A 52
  • B 45
  • C 3
  • D 12
Solution:
1328 Upvotes Verified Answer
The correct answer is: 12

(2cos218°-sin18)(cosθ+32cos(θ+π4)+3)

=(1+cos36°-sin18)(cosθ+32cos(θ+π4)+3)

=1+5+14-5-14cosθ+32cos(θ+π4)+3

Now, using cos(A+B)=cosAcosB-sinAsinB, we get

32cosθ+32cosθcosπ4-sinθsinπ4+3

=32cosθ+32cosθ 12-sinθ 12+3

=324cosθ-3sinθ+3

We know that if acosθ+bsinθ, then maximum value =a2+b2

So, maximum value of 

2cos218°- sin18°cosθ+32 cosθ+π4+3 is

32(5+3)=12

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