Cot Pi 2

sin (Ã Â € / 2x) nurture (Ã € / 2 + x) = sinx? 3

Relevant triangles and corresponding angles

Note that there is a phase difference of pi / 2 (offset) between the sign and the cosine, so if they have a phase difference of pi / 2, they can be written as relative to each other. As a result, you'll find the following relationship:

sin (pi / 2x) = cos (x)

sin (pi / 2 + x) = cos (x)

cos (pi / 2 + x) = sin (x)

We know that tan (x) = sin (x) / cos (x) and

Cot (x) = cos (x) / sin (x), then

Cot (pi / 2 + x) = cos (pi / 2 + x) / (sin (pi / 2 + x))

To prove this identity, simply prove that the expression on the left is reduced to sin (x).

sin (pi / 2 x) cot (pi / 2 + x) = cos (x) * (sin (x) / cos (x))

= Sin (x)

Sin (Ã Â € / 2 x) = cos (x)

Bed (Ã € / 2 + x) = {Bed (Ã € / 2) * Bed (x) 1} / {Bed (Ã € / 2) + Bed (x)

Base (Ã € / 2) = 0

Base (Â Â € / 2 + x) = 1 / base (x) = senx / cosx

As a result

sin (Ã € / 2x) cot (Ã € / 2 + x) = cos (x) (sinx / cosx) = sinx

Try.