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)