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SOME IMPORTANT MATHEMATICAL FORMULAE

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Published in: Mathematics
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Basic Math Formula

Anku S / Bhopal

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Qualification: B.Tech/B.E. (National Institute of Technology - 2016)

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  1. Area of a sector of a circle Arc length, S = r 0. adj opp sino ,cos0 — ,tan0 ,cote , seco , cosece -1. TRIGNOMETRY 1 = —r2e . 2 adj hyp opp hyp hyp 1 Sino or cosec0 cos eco 1 tano — or cote — adj 1 , cos0 — adj opp 1 or seco 1 1 sin 0 sec 0 cos0 sin 0 cose tano — , cote — cot 0 tan 0 cos 0 sin 0 sin20 + cos20 — sin20 — l- cos20; cos20 l- sin20; sec20 - tan20 = l; sec20 = 1+ tan20; tan20 = sec20 — l; cosec20 - cot20 — l; cosec20 1+ cot20; cot20 cosec20 STANDARD ANGLES 00 or 0 300 or 6 450 or 4 1 1 1 1 600 or 3 2 1 2 1 1 2 900 or 1 o o 1 2 Sin cos 1 Tan Cot sec 1 Cosec 1 2 3 2 1 2 2 50 or — 12 us-I 205 us-I us-I hyp opp 50 or — 12 6+1 6-1 VS-I vs-I ALLIED ANGLES Trigonometric functions of angles which are in the 2nd, 3rd and 4th quadrants can be obtained as follows : If the transformation begins at 900 or 2700, the trigonometric functions changes as sin cos tan cot sec 4+ cosec
  2. where as the transformation begins at 1800 or 3600, the same trigonometric functions will be retained, however the signs (+ or -) of the functions decides ASTC rule. COMPOUND ANGLES Sin(A+B)=sinAcosB+cosAsinB. Sin(A-B)= sinAcosB-cosAsinB. tan A + tan B I tan A tan B tan A tan B tan(A-B)= I + tan A tan B 1 + tan A tan — + A 4 I — tan A I tan A tan E —A 4 I + tan A tan A + tan B + tan C tan A tan B tan C tan(A+B+C)— I (tan A 'tan B + tan B tan C + tan C tan A) sin(A+B) sin(A-B)—sin2 A sin2 B = cos2 B —coe A cos(A+B) cos(A-B)- coe A - sin2 B MULTIPLE ANGLES 2 tan A I -sin 2A—2 sinA cosA. 2. sin 2A= I + tan2 A 3.cos 2A =cos2 A — sin2 A =1-2 sin 2 A . = 2cos2 A-I I tan 2 A I + tan2 A 2 tan A 4. tan 2A— 7. I-cos 2A 10. I-sin 2A- 12. sin 3A- I— tan2 A ' = 2 sin 2 A, 3 sin A 5. 1+cos 2A-2cos2 A, 6. coe A cos2A). 8. sin 2 cos2A) , 9.1+sin 2A—(sinA + cos (cosA — sin =(sinA — cos A)2, ll.cos 3A—4cos3 A—3cosA, 3 tan A tan3 A -4sin3A, 13.tan3A- I 3 tan2 A
  3. HALF ANGLE FORMULAE 4) cose = I—2sin 2 tan 2 l) sin 0—2 sin —cos — 2) sin 0= 2 5) cos 2 cos 2 2 tan I + tan2 . 3) coso= 6) cose = cos2@—sin 2 2 2 29—1. 2 I — tan2 I + tan2 2 2 7) tan e = 2 2 1 — tan 2 8) l+coso= 2 cos 2 — cose = 2 sin 2 PRODUCT TO SUM 2 sinA COSB = sin(A+B) + sin(A-B). 2 cosA sinB = sin(A+B) - sin(A-B). 2 cosA cosB - cos(A+B) + cos(A-B). 2 sinA sinB = SUM TO PRODUCT C+D C-D Sin C + sin D =2sin 2 cos 2 C+D C-D sin Sin C —sin D —2 cos 2 2 C+D C-D cos c + D cos C- cos D cos C- cos D = = 2 cos 2 cos 2 C-D C+D ——2 sin 2 sm 2 PROPERTIES AND SOLUTIONS OF TRIANGLE a b c sin A sin B sin C Cosine Rule: a2 b2+ c2 -2bc cosA or Sine Rule: triangle. = 2R , where R is the circum radius of the b2 +c2 —a 2 cosA — 2bc
  4. -2ac cosB or -2ab cosc or Projection Rule: a = b cosc +c cosB b = c COSA +a cosc c = a cosB +b COSA Tangents Rule: a cosB - cosc = +c2 —b2 2ac 2 2ab B—C tan 2 C-A 2 tan 2 cot b+c 2 cot 2 cot 2 Half angle formula: A cos 2 B , cos 2 c , cos 2 Area of triangle ABC = — bc sin A = — ac sin B = —ab sin C . A sin 2 sin 2 c sin 2 bc ac ab bc s(s —b) ab s(s c) , A 2 tan 2 c tan 2 s(s —a) s(s b) s(s c) Area of triangle ABC —

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