How to find the exact value of cos(30* + 45*)?

Question

How to find the exact value of cos(30* + 45*)?

Answer 1

= cos 30 cos 45 - sin 30 sin 45

= sqrt(3)/2 */1 sqrt (2) - 1/2 *1/ sqrt(2)

= (sqrt(3) - 1)/ (2*sqrt(2))

using cos (A+B)= cos A cos B - sin A sin B

and knowing the value of cos 30 sin 30 cos 45 sin 45

math kp

Answer 2

the exact value is cos(75°). There is no other way to represent the exact value, because the answer is an irrational number. If you want to represent it as a decimal number, you would be writing numbers until the end of time.

Answer 3

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

cos(30+45)=cos(30)cos(45)-sin(30)sin(4...

cos(30)= √3/2

cos(45)= 1/ √2

sin(30)=1/2

sin(45)=1/ √2

(√3/2) ( 1/√2) - (1/2)( 1/√2)

= (√3-1) / 2√2