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From the following options, find the value of $sin 18 ° cos 72 °$ .

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sin 72 °

cos 18 °

answer is C.

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Detailed Solution

Given that,

sin 18 ° cos 72 °

.
We know that, the complementary formula for

sin θ

is:

sin (90 ° − θ) = cos θ

Convert

sin θ

into

cos θ

trigonometric function.

⇒ sin 18 ° cos 72 ° = sin (90 ° − 72 °) cos 72 °

Apply complementary angle formula,

⇒ sin 18 ° cos 72 ° = cos 72 ° cos 72 ° ⇒ sin 18 ° cos 72 ° = 1

Thus,

sin 18 ° cos 72 ° = 1

.
Hence, option 3) is correct.

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