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Question

Assertion :Let f(θ)=5cosθ+3cos(θ+π3),then4f(0)10 Reason: The maximum & minimum values of acosx±bsinx+c are ca2+b2 and c+a2+b2

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion false but Reason is true
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Let P(x)=acosx±bsinx, let a=rcosα,b=rsinα
r=a2+b2,tanα=ba
P(x)=r(cosαcosx±sinαsinx)=rcos(x±α)
rp(x)r values of x
Now f(θ)=5cosθ+3cos(θ+π3)+3
=5cosθ+32cosθ332sinθ+3
=132cosθ332sinθ+3
3 (132)2+(332)2f(θ)3+ (132)2+(332)2
4f(θ)10

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