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Measurement of Angle ,Trigonometric Ratios and equation | free study Material for IIT-JEE , NDA and Airforce | SAT | CBSE


Measurement of Angle ,Trigonometric Ratios and equation

⚫Relation Between Degree and Radians degree_and_radian_relation
⚫ Relation Between Trigonometrical Ratios and Right Angled Triangle Side right_angled_triangle Relation Between Trigonometrical Ratios and Right Angled Triangle Side
⚫ Relation Between Trigonometrical Ratios sinθ.cosecθ = 1
tanθ.cotθ = 1
cosθ.secθ = 1
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
⚫ Fundamental trigonometric Identities : sin2θ + cos2θ = 1
tan2θ + 1 = sec2θ
1 + cot2θ = cosec2θ
⚫ Trigonometrical ratios for various angles

⚫ Formula For the trigonometric ratios of sum and difference of two angles sin(A+B) = sinA cosB + cosA sinB
sin(A-B) = sinA cosB - cosA sinB
cos(A+B) = cosA cosB - sinA sinB
cos(A-B) = cosA cosB + sinA sinB
sin(A+B).sin(A-B) = sin2A - sin2B = cos2B - cos2A
cos(A+B).cos(A-B) = cos2A - sin2B = cos2B - sin2A
⚫ Formulae to transform the product into sum or difference
⚪ 2sinAcosB = sin (A+B) + sin(A-B)
⚪ 2cosA sinB = sin(A+B) -sin(A-B)
⚪ 2cosAcosB = cos(A+B)+ cos(A-B)
⚪ 2sinAsinB = cos(A+B) - cos(A-B)
⚫ Formulae to transform the sum or difference into product :
⚫ Trigonometric ration of multiple of an angle :
⚪ sin2A = 2sinAcosA
⚪ cos2A = cos2A - sin2A = 2cos2A -1 = 1 - 2sin2A
⚪ sin3A = 3sinA - 4sin3A
⚪ cos3A = 4 cos3 - 3 cosA
⚫ Triangle Related trigonometric Formulae :
IF x + y + z = 1800 ⚪ tanx + tany + tanz = tanxtany tanz
⚪ cotx coty + cotx cotz + coty cotz = 1

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