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Question

tan54° can be expressed as


A

(cos9°+sin9°)(cos9°sin9°)

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B

(cos9°-sin9°)(cos9°+sin9°)

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C

(sin9°-cos9°)(cos9°+sin9°)

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D

None of these

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Solution

The correct option is A

(cos9°+sin9°)(cos9°sin9°)


Solving function using trigonometric identities:

We know, tan(A+B)=(tanA+tanB)(1tanAtanB)

tan54°=tan(45+9)°

=(tan45°+tan9°)(1tan45°tan9°)

=(1+tan9°)(1tan9°)

=1+sin9°cos9°1sin9°cos9°

=(cos9°+sin9°)(cos9°sin9°)

Hence, the option (A) is the answer.


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