Question

Compute cos 345 from the functions of 300 and 45

Answer 1

Given:  cos 345 degree

To find: Compute cos 345 from the functions of 300 and 45

Solution:

• Now cos 345 can be written as cos(300 + 45)

• Now using the formula:

                cos(A-B) = cos A . cos B − sin A . sin B, we get:

                cos 300° . cos 45° - sin 300° . sin 45°

• Now putting the standard values, we get:

                cos 300° (1/√2) - sin 300°(1/√2)

                1/√2(cos 300° - sin 300°)

• Now 300 can be written as 360 - 60, so we have:

                1/√2(cos (360 - 60) - sin (360 - 60))

• Now we know cos(360 - x) = cos x and sin (360 - x) = - sin x

                1/√2(cos 60 + sin 60)

                1/√2(1/2 + √3/2)

                √3 + 1 / 2√2

• Rationalising the denominator, we get:

                (√3 + 1 / 2√2) x √2/√2

                √6 + √2 / 4

Answer:

             So the value of cos 345 is √6 + √2 / 4

Answer 2

Step-by-step explanation:

by use the formula given

and then follow other steps