Question

angle difference identity to find the exact value of;
cos 75°.

Answer 1

Can't you just use a calculator to find \(\sf cos(75^o)\)?

Answer 2

i need to use angle difference identity to solve it.

Answer 3

yes look cos(120-45)=cos(120)cos(45)+sin(120)sin(45)

Answer 4

is that what you want

Answer 5

it ca be written as cos(30+45)

Answer 6

Yes..^^^

Answer 7

We have:

\(\sf cos(30^o + 45^o) = cos(30^o)cos(45^o) - sin(30^o)sin(45^o)\)

Which gives us:

\(\dfrac{\sqrt3}{2} \times \dfrac{\sqrt2}{2} - \dfrac{1}{2} \times \dfrac{\sqrt2}{2}\)

Answer 8

Can you simplify that? @secretslocked

Answer 9

igreen did you read ? angle "DIFFERENCE"

Answer 10

Oh..I'm doing Angle-Sum..sorry.

Answer 11

so you should do cos(120-45)=-cos(60)cos(45)+sin(60)sin(45)

Answer 12

@joyraheb why 60?

Answer 13

because cos(120)=cos(180-60)=-cos(60)
understood?

Answer 14

sort of

Answer 15

and sin(120)=sin(180-60)=sin(60)

Answer 16

and you know sin(60)=√3/2 and cos(60)=1/2

Answer 17

and cos(45)=sin(45)=√2/2 and thats it now just replace and youll get cos(75)