From the following options, the value of $tan 63 ° ⋅ tan 27 °$ is:

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tan 63 °

cot 27 °

answer is C.

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Detailed Solution

Given that,

tan 63 ° ⋅ tan 27 °

.
Write complementary angle formula for

tan θ

,
We know that,

tan θ = cot (90 ° − θ)

.
Convert

tan θ

in terms of

cot θ

trigonometric function in LHS.
Apply complementary function for tan,

⇒ tan 63 ° ⋅ tan 27 ° =cot(90 ° − 63 °) . t a n 27 ° ⇒ tan 63 ° ⋅ tan 27 ° = cot27 ° . t a n 27 ° Since tan θ = 1 cot θ,

⇒ tan 63 ° ⋅ tan 27 ° = cot27 ° . 1 cot 27 °

⇒ tan 63 ° ⋅ tan 27 ° = cot27 ° . 1 cot 27 ° ⇒ tan 63 ° ⋅ tan 27 ° = 1

The value of

tan 63 ° ⋅ tan 27 °

is 1.
Hence, option 3) is correct.

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