A physicist needs to calculate the exact value of a force(measured in newtons) in the horizontal direction with the expression 25cos75. Simplify the expression to find the exact value

25*√((2-√3)/2)

Step-by-step explanation:

Use the identity: cos(x)=sin(90°-x)

cos(75°)=sin(90°-75°)=25sin(90°-75°)

Simplify

25sin(15°)

then write sin(15°) as sin(30°/2)

Use the half-angle identity: sin(x/2)= ((1-cos(x))/2)^(1/2)

((1-cos(30°))/2)^(1/2)     cos(30°)=((3)^(1/2))/2

then plug that in for the cos(30°) and solve

√((2-√3)/2)    multiply by 25

25*√((2-√3)/2)

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

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step-by-step explanation: