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Question

(cos9°+sin9°)(cos9°-sin9°) is equal to


A

tan26°

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B

tan81°

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C

tan51°

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D

tan54°

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E

tan46°

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Solution

The correct option is D

tan54°


Explanation or the correct option:

Solve the expression (cos9°+sin9°)(cos9°sin9°)

By Divide the numerator and denominator by cos 9°, we get

cos9°cos9°+sin9°cos9°cos9°cos9°sin9°cos9°

=(1+tan9°)(1tan9°)

=(tan45°+tan9°)[1tan9°×(1)] ; tan45°=1

=(tan45°+tan9°)(1tan9°tan45°)

=tan(45°+9°) ; tanA+tanB1-tanAtanB=tan(A+B)

=tan54°

Hence, Option ‘D’ is Correct.


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