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From the following options, find the value of $sin 54 ° − cos 36 °$ .

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sin 36 °

cos 54 °

answer is D.

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Detailed Solution

Given that,

sin 54 ° − cos 36 °

.
We know that, the complementary formula for

sin θ

is:

sin (90 ° − θ) = cos θ

Convert

sin θ

into

cos θ

trigonometric function.

⇒ sin 54 ° − cos 36 ° = sin (90 ° − 36 °) − cos 36 °

Apply complementary angle formula,

⇒ sin 54 ° − cos 36 ° = cos 36 ° − cos 36 ° ⇒ sin 54 ° − cos 36 ° = 0

Thus,

sin 54 ° − cos 36 ° = 0

.
Hence, option 4) is correct.

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