Question

cos75degrees-cos15degrees?

Answer 1

\[\large \cos(C) - \cos(D) = 2 \sin(\frac{C+D}{2}) \sin (\frac{D-C)}{2}\]

Here C is 75 and D is 15..

Try to use the formula now..

Answer 2

Thanks!

Answer 3

-.75. But that doesn't match up to my options :/
a. sqrt6/2
b. sqrt2/2
c. -sqrt6/2
d. -sqrt2/2

Answer 4

The answer will be in negative..

Answer 5

c.=-1.73
d.=-1

Answer 6

\[\cos(75) - \cos(15) = 2 \sin(\frac{90}{2}) \sin (\frac{-60}{2})\]

\[\implies 2 \sin(45) \sin(-60)\]

Remember: \(sin(-\theta) = -sin(\theta)\)

So:

\[\implies -2 \sin(45)\sin(60)\]

\[\large \sin(45) = \frac{1}{\sqrt{2}}\]

\[\large \sin(60) = \frac{\sqrt{3}}{2}\]

Plug these values there..

Answer 7

Then simplified and the end result is c. Can you please clarify @waterineyes

Answer 8

\[\implies -2 \times \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} \implies - \frac{\sqrt{3}}{\sqrt{2}}\]

\[\implies - \frac{\sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} \implies \color{green}{- \frac{\sqrt{6}}{2}}\]

Answer 9

Yes it is C..