MATHS FORMULA
(a+b+c)²= a²+b²+c²+2(ab+bc+ca)
1. (a+b)²= a²+2ab+b²
2. (a+b)²= (a-b)²+4ab
3. (a-b)²= a²-2ab+b²
4. (a-b)²= (a+b)²-4ab
5. a² + b²= (a+b)² - 2ab.
6. a² + b²= (a-b)² + 2ab.
7. a²-b² =(a + b)(a - b)
8. 2(a² + b²) = (a+ b)² + (a - b)²
9. 4ab = (a + b)² -(a-b)²
10. ab ={(a+b)/2}²-{(a-b)/2}²
11. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
12. (a + b)³ = a³ + 3a²b + 3ab² + b³
13. (a + b)³ = a³ + b³ + 3ab(a + b)
14. (a-b)³=a³-3a²b+3ab²-b³
15. a³ + b³ = (a + b) (a² -ab + b²)
16. a³ + b³ = (a+ b)³ -3ab(a+ b)
17. a³ -b³ = (a -b) (a² + ab + b²)
18. a³ -b³ = (a-b)³ + 3ab(a-b)
Sin0° =0
Sin30° = 1/2
Sin45° = 1/√2
Sin60° = √3/2
Sin90° = 1
Cos is opposite of sin
tan0° = 0
tan30° = 1/√3
tan45° = 1
tan60° = √3
tan90° = ∞
cot is opposite of tan
sec0° = 1
sec30° = 2/√3
sec45° = √2
sec60° = 2
sec90° = ∞
cosec is opposite of sec
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)+cos(A-B)
2sinAsinB=cos(A-B)-cos(A+B)
Sin(A+B)=sinA cosB+ cosA sinB.
» cos(A+B)=cosA cosB - sinA sinB.
» sin(A-B)=sinAcosB-cosAsinB.
» cos(A-B)=cosAcosB+sinAsinB.
» tan(A+B)= (tanA + tanB)/ (1−tanAtanB)
» tan(A−B)= (tanA − tanB) / (1+ tanAtanB)
» cot(A+B)= (cotAcotB −1) / (cotA + cotB)
» cot(A−B)= (cotAcotB + 1) / (cotB− cotA)
» Sin(A+B)=sinA cosB+ cosA sinB.
» cos(A+B)=cosA cosB +sinA sinB.
» sin(A-B)=sinAcosB-cosAsinB.
» cos(A-B)=cosAcosB+sinAsinB.
» tan(A+B)= (tanA + tanB)/ (1−tanAtanB)
» tan(A−B)= (tanA − tanB) / (1+ tanAtanB)
» cot(A+B)= (cotAcotB −1) / (cotA + cotB)
» cot(A−B)= (cotAcotB + 1) / (cotB− cotA)
a/sinA = b/sinB = c/sinC = 2R
» a = b cosC + c cosB
» b = a cosC + c cosA
» c = a cosB + b cosA
» cosA = (b² + c²− a²) / 2bc
» cosB = (c² + a²− b²) / 2ca
» cosC = (a² + b²− c²) / 2ca
» Δ = abc/4R
» sinΘ = 0 Then,Θ = nΠ
» sinΘ = 1 Then,Θ = (4n + 1)Π/2
» sinΘ =−1 Then,Θ = (4n− 1)Π/2
» sinΘ = sinα Then,Θ = nΠ (−1)^nα
1. sin2A = 2sinAcosA
2. cos2A = cos²A − sin²A
3. cos2A = 2cos²A − 1
4. cos2A = 1 − sin²A
5. 2sin²A = 1 − cos2A
6. 1 + sin2A = (sinA + cosA)²
7. 1 − sin2A = (sinA − cosA)²
8. tan2A = 2tanA / (1 − tan²A)
9. sin2A = 2tanA / (1 + tan²A)
10. cos2A = (1 − tan²A) / (1 + tan²A)
11. 4sin³A = 3sinA − sin3A
12. 4cos³A = 3cosA + cos3A
» Sin²Θ+Cos²Θ=1
» Sec²Θ-tan²Θ=1
» Cosec²Θ-Cot²Θ=1
» SinΘ=1/CosecΘ
» CosecΘ=1/SinΘ
» CosΘ=1/SecΘ
» SecΘ=1/CosΘ
» tanΘ=1/CotΘ
» CotΘ=1/tanΘ
» tanΘ=SinΘ/CosΘ
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