What is the value of cos 75°?

We need to find the value of cos 75

cos 75= cos (30+45)

The values of sin 45, sin 30, cos 45 and cos 30 are commonly known.

We use these to determine the value of cos 75 and sin 75.

We know the identity

cos (x + y) = (cos x)*(cos x) – (sin x)(sin y) cos 75

os 75 = cos (30 + 45)

(cos 30)(cos 45) – (sin 30)(sin 45)

The values of cos and sin 30 also cos and sin 345 are listed below

cos 30 = √3 /2

sin 30 = 1/2,

sin 45 = cos 45 = 1/√2

=√3/2√2 – 1/2 X √2

=[√(3) – 1]/2√2

Answer

Hence

cos 75= [√(3) – 1]/2√2

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