Find the value of sin75°.

Trigonometry deals with the measurement of angles and helps us study the relationship between the sides and angles of a right-angled triangle.

Answer: The value of sin75° is (√3 + 1)/ (2√2).

Let's look into the steps to find the value of sin 75°.

Explanation:

We can write sin 75° as,

sin 75° = sin (45° +30° )

We know that,

sin (A + B) = sin A. cos B + cos A. sin B

Thus, sin (45° + 30° ) = sin 45° . cos 30° + cos 45° . sin 30° ------------ (1)

From trigonometric table, we have the following values,

sin 30° = 1/2, sin 45° = 1/√2, cos 30° = √3/2 and cos 45° = 1/√2 

Substituting these values in (1) we get,

⇒ sin (45° + 30° ) = 1/√2 . √3/2 + 1/√2 . 1/2

⇒ sin (45° + 30° ) = (√3 + 1) / 2√2

⇒ sin 75° = (√3 + 1) / 2√2

Hence, the value of sin75° is (√3 + 1)/ (2√2).