Trigonometry formulas - at a glance

Higher Mathematics (H.S.C) — Trigonometry Formula Sheet


TRIGONOMETRY
Formula Reference Sheet • Higher Mathematics (H.S.C)


1. Sum and Difference Formulas
1.1 Sine
sin(A + B) = sinA·cosB + cosA·sinB sin(A − B) = sinA·cosB − cosA·sinB


1.2 Cosine
cos(A + B) = cosA·cosB − sinA·sinB cos(A − B) = cosA·cosB + sinA·sinB


1.3 Tangent
tan(A + B) = (tanA + tanB) / (1 − tanA·tanB) tan(A − B) = (tanA − tanB) / (1 + tanA·tanB)


1.4 Cotangent
cot(A + B) = (cotA·cotB − 1) / (cotB + cotA) cot(A − B) = (cotA·cotB + 1) / (cotB − cotA)



2. Product of Sum and Difference
sin(A+B)·sin(A−B) = sin²A − sin²B = cos²B − cos(A+B)·cos(A−B) = cos²A − sin²B = cos²B −
cos²A sin²A


tan(A+B)·tan(A−B) = (tan²A − tan²B) / (1 − cot(A+B)·cot(A−B) = (cot²A·cot²B − 1) / (cot²B −
tan²A·tan²B) cot²A)



3. Product-to-Sum Formulas
2·sinA·cosB = sin(A+B) + sin(A−B) 2·sinB·cosA = sin(A+B) − sin(A−B)


2·cosA·cosB = cos(A+B) + cos(A−B) 2·sinA·sinB = cos(A−B) − cos(A+B)



4. Sum-to-Product Formulas
sinC + sinD = 2·sin½(C+D)·cos½(C−D) sinC − sinD = 2·cos½(C+D)·sin½(C−D)


cosC + cosD = 2·cos½(C+D)·cos½(C−D) cosC − cosD = 2·sin½(C+D)·sin½(D−C)




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