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Question

# Assertion :If exp{{sin2x+sin4x+sin6x+.....inf}loge2} satisfies the equation x2−9x+8=0, then the value of cosxcosx+sinx is √3−12(0<x<π/2) Reason: sin2x+sin4x+sin6x+.... ∞=sec2x

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 is incorrect but Reason is correct
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Solution

## The correct option is C Assertion is correct but Reason is incorrectExp{(sin2x+sin4x+sin6x+....∞)loge2}=esin2x1−sin2xloge2=esin2xcos2xloge2⇒2tan2x satisfy x2−9x+8=0⇒x=1,8∴2tan2x=1 and 2tan2x=8⇒tan2x=0 and tan2x=3⇒x=nπ and tan2x=(tanπ3)2⇒x=nπ and x=nπ±π3Neglecting x=nπ as ⇒x=π3∈(0,π2)∴cosxcosx+sinx=1212+√32=11+√3=√3−13−1=√3−12

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