Find in terms of trigonometric function of x

Tan(90° + x)

To find the value of tan(90° + x) in terms of trigonometric functions of x, we can use the identity: tan(90° + x) = -cot(x)

To understand how we arrive at this result, let's consider the definitions and properties of the tangent and cotangent functions:

The tangent function (tan) is defined as the ratio of the sine of an angle to its cosine: tan(x) = sin(x) / cos(x).

The cotangent function (cot) is defined as the reciprocal of the tangent: cot(x) = 1 / tan(x).

Now, substituting x = (90° + x) into the definition of cotangent, we get: cot(90° + x) = 1 / tan(90° + x).

Using the identity for cotangent, we can rewrite this as:
cot(90° + x) = 1 / tan(90° + x) = cot(-x) = -cot(x).

Therefore, tan(90° + x) can be expressed as -cot(x) in terms of trigonometric functions of x.