Question

Find the value of Cos 75​

Answer 1

Answer:

We can write 75o as the sum of 45o and 30o

Therefore,

cos 75o = cos (30+45)o

From trigonometric formulae,

cos (x + y) = cos x cos y - sin x sin y

Taking x = 30 and y = 45 we get,

cos 75o = cos (30 + 45)o

cos 75o = cos 30o × cos 45o – sin 30o × sin 45o --------(i)

From trigonometric table values we have,

cos 30o = √3 /2

sin 30o = 1/2

sin 45o = cos 45o = 1/√2

Substituting these values in equation (i)

cos 75o = √3/2 × 1/√2 – 1/2 × 1/√2

⇒ cos 75o = (√3-1) / 2√2

Thus, the value of cos 75o is (√3-1) / 2√2.

Answer 2

Answer:

cos 75°= cos(45°+30°)

=cos 45° cos 30° - sin 45° sin 30°

=1/✓2. × ✓3/2 - 1/✓2 × 1/2

=✓3-1/2✓2