Question

please help!

k = (cos 25° cos 35°) / (cos 10° sin 20°) . so, cos 10° equal to....
a. (k√3+1)/(2k-2)
b. (k√3+1)/(2k+1)
c. (k√3+1)/(2k+2)
d. (k√3+1)/(k+1)
e. (k√3+1)/(k-1)
(choose one option that is correct and give the explanation)

Answer 1

TRUST ME....I have spent hours on this. I can tell you with certainty that none of the options is correct.

You can readily solve for k = 2.2041293991
None of the options are equal to cos10º = 0.984807753

2.2041293991 k
0.984807753 cos10º

2.000476074 a
0.8907976274 b
0.7517898789 c
1.5035797577 d
4.000952148 e

Answer 2

I concur. If you explicitly calculate the value of k with the given information you get k ≈ 2.2, and
k√3 + 1 ≈ 4.8 .

Solving for your choices a thru e gives a ≈ 2, d ≈ 1.5, and e ≈ 4. Clearly none of these will work as neither the sine nor the cosine function can take on a value > 1.

That leaves b ≈ 0.89, corresponding to an angle of 27° and c ≈ 0.75, corresponding to an angle of 41° when solving for cos Θ...