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Trigonometric function in high school mathematics (full mark)
Formula of trigonometric function?

Two-angle sum formula?

Sin (A+B)? =? sinAcosB+cosAsinB?

Sin (A-B)? =? sinAcosB-cosAsinB?

cos(A+B)? =? cosAcosB-sinAsinB?

cos(A-B)? =? cosAcosB+sinAsinB?

Tan (A+B)? =? (tanA+tanB)/( 1-tanAtanB)?

Tan ()? =? (tanA-tanB)/( 1+tanAtanB)?

cot(A+B)? =? (cotAcotB- 1)/(cotB+cotA)?

Kurt (A-B)? =? (cotAcotB+ 1)/(cotB-cotA)?

Double angle formula?

tan2A? =? 2tanA/( 1-tan^2? a)?

Sin2A=2SinA? CosA?

Cos2A? =? Cos^2? Sin^2? Answer?

=2Cos^2? A— 1?

= 1—2sin^2? Answer?

Triple angle formula?

sin3A? =? 3sina-4(sina)^3; ?

cos3A? =? 4(cosA)^3? -3cosA?

tan3a? =? Tan? Answer? tan(π/3+a)tan(π/3-a)?

Half angle formula?

Sin (A/2)? =? √{( 1 - cosA)/2}?

cos(A/2)? =? √{( 1+cosA)/2}?

Tan (one/two)? =? √{( 1-cosA)/( 1+cosA)}?

cot(A/2)? =? √{( 1+cosA)/( 1-cosA)}?

Tan (one/two)? =? (1-cosA)/ Sina = Sina /( 1+cosA)?

Sum-difference product

Sin (a)+ sin (b)? =? 2sin[(a+b)/2]cos[(a-b)/2]?

Sin (1)-Sin (2)? =? 2cos[(a+b)/2]sin[(a-b)/2]?

cos(a)+cos(b)? =? 2cos[(a+b)/2]cos[(a-b)/2]?

cos(a)-cos(b)? =? -2sin[(a+b)/2]sin[(a-b)/2]?

tanA+tanB=sin(A+B)/cosAcosB?

Product and difference?

Crime (a) and crime (b)? =? - 1/2*[cos(a+b)-cos(a-b)]?

cos(a)cos(b)? =? 1/2*[cos(a+b)+cos(a-b)]?

sin(a)cos(b)? =? 1/2*[sin(a+b)+sin(a-b)]?

Cos(a) crime (b)? =? 1/2*[sin(a+b)-sin(a-b)]?

Inductive formula?

Sin (-a)? =? -sin (1)?

cos(-a)? =? cos(a)?

sin(π/2-a)? =? cos(a)?

cos(π/2-a)? =? Crime (1)?

sin(π/2+a)? =? cos(a)?

cos(π/2+a)? =? -sin (1)?

sin(π-a)? =? Crime (1)?

cos(π-a)? =? -cos(a)?

sin(π+a)? =? -sin (1)?

cos(π+a)? =? -cos(a)?

tgA=tanA? =? Sina /cosA?

Universal formula?

Crime (1)? =? [2tan(a/2)]? /? { 1+[tan(a/2)]^2}?

cos(a)? =? { 1-[tan(a/2)]^2}? /? { 1+[tan(a/2)]^2}?

Tan (1)? =? [2tan(a/2)]/{ 1-[tan(a/2)]^2}?

Other recipes?

Answer? Sin (a)+b? cos(a)? =? [√(a^2+b^2)]*sin(a+c]? [where tan(c)=b/a]?

Answer? Crime (A)-B? cos(a)? =? [√(a^2+b^2)]*cos(a-c]? [where tan(c)=a/b]?

1+sin(a)? =? 【sin(a/2)+cos(a/2)]^2; ?

1-sin(a)? =? 【sin(a/2)-cos(a/2)]^2; ; ?

Other non-critical trigonometric functions?

csc(a)? =? 1/sin(a)?

sec(a)? =? 1/cos(a)?

Hyperbolic function?

Singh (a)? =? [e^a-e^(-a)]/2?

cosh(a)? =? [e^a+e^(-a)]/2?

tg? h(a)? =? Sin? h(a)/cos? h(a)?

Formula 1:?

Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:?

sin(2kπ+α)=? sinα?

cos(2kπ+α)=? cosα?

tan(2kπ+α)=? tanα?

cot(2kπ+α)=? cotα?

Formula 2:?

Let α be an arbitrary angle. What is the relationship between the trigonometric function value of π+α and that of α?

sin(π+α)=? -Xin α?

cos(π+α)=? -cosα?

tan(π+α)=? tanα?

cot(π+α)=? cotα?

Formula 3:?

Arbitrary angle α sum? The relationship between trigonometric function values of-α:?

sin(-α)=? -Xin α?

cos(-α)=? cosα?

tan(-α)=? -tanα?

cot(-α)=? -cotα?

Formula 4:?

The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:?

sin(π-α)=? sinα?

cos(π-α)=? -cosα?

tan(π-α)=? -tanα?

cot(π-α)=? -cotα?

Formula 5:?

Using formula-and formula 3, we can get the trigonometric function value of 2π-α and α:?

sin(2π-α)=? -Xin α?

cos(2π-α)=? cosα?

tan(2π-α)=? -tanα?

cot(2π-α)=? -cotα?

Equation 6:?

The relationship between π/2 α and 3 π/2 α and the trigonometric function value of α:?

sin(π/2+α)=? cosα?

cos(π/2+α)=? -sinα