Which value is equivalent to cos15∘?

a. sin45∘
b.sin75∘
c. sin85∘
d. sin30∘

Cos15 = the sine of its' complimentary angle which is 75o.

Yeah the answer is sin 75.

Well, well, well, let's put on our math hats and have some fun, shall we? Now, to find the value equivalent to cos(15°), we need to look at our options here.

Starting with a, sin(45°). Oh dear, I'm afraid that's not quite right. The cosine of 15° is definitely not the same as the sine of 45°.

Moving on to b, sin(75°). Ah, no dice on this one either. The cosine of 15° is sneaky, it doesn't match up with the sine of 75°.

Now, let's give c a whirl. Sin(85°). Oh my, this option doesn't align either. The cosine of 15° doesn't see eye to eye with the sine of 85°.

Finally, we've got d, sin(30°). Ah, it seems like we've struck humor gold! The value equivalent to cos(15°) is indeed the same as the sine of 30°! Hooray for d!

So, my dear friend, the correct answer is d. The value equivalent to cos(15°) is sin(30°).

To find the equivalent value of cos 15°, we can use the trigonometric identity:

cos (90° - θ) = sin θ

In this case, θ = 15°. So we can rewrite cos 15° as sin (90° - 15°):

cos 15° = sin (90° - 15°)

simplifying:

cos 15° = sin 75°

Therefore, the value equivalent to cos 15° is sin 75°.

So the correct answer is b. sin 75°.

To determine which value is equivalent to cos15∘, we need to use trigonometric identities and formulas. In this case, we can use the identity cos(90° - θ) = sinθ.

The given options are:
a. sin45∘
b. sin75∘
c. sin85∘
d. sin30∘

To find the equivalent value to cos15∘, we need to find the corresponding angle θ for each option and then apply the identity cos(90° - θ) = sinθ.

a. sin45∘:
To find the corresponding angle θ, we subtract 45° from 90°:
θ = 90° - 45° = 45°.

Now, applying the identity, we have:
cos15∘ = sin45∘.
However, sin45∘ ≠ cos15∘, so option a is not equivalent to cos15∘.

b. sin75∘:
To find the corresponding angle θ, we subtract 75° from 90°:
θ = 90° - 75° = 15°.

Now, applying the identity, we have:
cos15∘ = sin75∘.
Since 15° = 75°, option b is equivalent to cos15∘.

c. sin85∘:
To find the corresponding angle θ, we subtract 85° from 90°:
θ = 90° - 85° = 5°.

Now, applying the identity, we have:
cos15∘ = sin5∘.
Since 5° ≠ 15°, option c is not equivalent to cos15∘.

d. sin30∘:
To find the corresponding angle θ, we subtract 30° from 90°:
θ = 90° - 30° = 60°.

Now, applying the identity, we have:
cos15∘ = sin60∘.
Since 60° ≠ 15°, option d is not equivalent to cos15∘.

Therefore, the value equivalent to cos15∘ is sin75∘, so the correct answer is b.