Universal formulas include trigonometric functions and inverse trigonometric functions. In the universal formula, only tan(a/2) polynomial can glorify all trigonometric functions. Replacing sinα, cosα and tanα with a formula containing tan(α/2) is called universal substitution formula.

General formula commonly used in junior high school:

1、sinα=[2tan(α/2)]/{ 1+[tan(α/2)]^2}？

2、cosα=[ 1-tan(α/2)^2]/{ 1+[tan(α/2)]^2}？

3、tanα=[2tan(α/2)]/{ 1-[tan(α/2)]^2}？

Replacing sinα, cosα and tanα with tan(α/2) is called universal substitution formula.

Extended data:

Universal formula, only tan(a/2) polynomial can glorify all trigonometric functions. After using the general formula, all trigonometric functions are represented by tan(a/2).

For convenience, the letter T can be used instead, so that a trigonometric function formula becomes an algebraic formula with T, which can be solved by algebraic knowledge. The general formula makes up the gap between trigonometry and algebra.

Specific functions include the following four points:

1, and the unified angle is α/2;

2. unify the function name as tan；;

3. Any real number can be expressed in the form of tan(α/2) (except special ones) and can be exchanged by tangent function;

4. In some integrals, integrals with trigonometric functions can be transformed into integrals with fractions.

Baidu Encyclopedia-Universal Formula