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Sine=OppositeHypotenuseSecant=HypotenuseAdjacentCosine=AdjacentHypotenuseTangent=OppositeAdjacentCo−Secant=HypotenuseOppositeCo−Tangent=AdjacentOpposite The reciprocal identities are given as:CosecΘ=1sinΘsecΘ=1cosΘcotΘ=1tanΘsinΘ=1CosecΘcosΘ=1secΘtanΘ=1cotΘAll these are taken from a right angled triangle. With the length and base side of the right triangle given, we can find out the sine, cosine, tangent, secant, cosecant and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the trigonometric functions.Basic Trigonometry Formulas:A.Trigonometry Formulas involving Periodicity Identities:sin(x+2π)=sinxcos(x+2π)=cosxtan(x+π)=tanxcot(x+π)=cotxAll trigonometric identities are cyclic in nature. They repeat themselves after this periodicity constant. This periodicity constant is different for different trigonometric identity.tan 45 = tan 225 but this is true for cos 45 and cos 225.Refer to the above trigonometry table to verify the values.B.Trigonometry Formulas involving Cofunction Identities – degree:sin(90∘−x)=cosxcos(90∘−x)=sinxtan(90∘−x)=cotxcot(90∘−x)=tanxC.Trigonometry Formulas involving Sum/Difference Identities:sin (x + y) = sin(x) cos(y) + cos(x) sin(y)cos(x + y) = cos(x) cos(y) – sin(x) sin(y)tan(x+y)=tanx+tany1−tanx⋅tanysin(x – y) = sin(x) cos(y) – cos(x) sin(y)cos(x – y) = cos(x) cos(y) + sin(x) sin(y)tan(x−y)=tanx−tany1+tanx⋅tanyD.Trigonometry Formulas involving Double Angle Identities:sin(2x) = 2 sin(x).cos(x)cos(2x)=cos2(x)–sin2(x),cos(2x)=2cos2(x)−1cos(2x)=1–2sin2(x)tan(2x)=[2tan(x)][1−tan2(x)]E.Trigonometry Formulas involving Half Angle Identities:sinx2=�1−cosx2‾‾‾‾‾‾√cosx2=�1+cosx2‾‾‾‾‾‾√tan(x2)=1−cos(x)1+cos(x)‾‾‾‾‾‾‾√Also, tan(x2)=1−cos(x)1+cos(x)‾‾‾‾‾‾‾√=(1−cos(x))(1−cos(x))(1+cos(x))(1−cos(x))‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=(1−cos(x))21−cos2(x)‾‾‾‾‾‾‾‾‾√=(1−cos(x))2sin2(x)‾‾‾‾‾‾‾‾‾√=1−cos(x)sin(x)So, tan(x2)=1−cos(x)sin(x)F.Trigonometry Formulas involving Product identities:sinx⋅cosy=sin(x+y)+sin(x−y)2cosx⋅cosy=cos(x+y)+cos(x−y)2sinx⋅siny=cos(x+y)−cos(x−y)2G.Trigonometry Formulas involving Sum to Product Identities:sinx+siny=2sinx+y2cosx−y2sinx−siny=2cosx+y2sinx−y2cosx+cosy=2cosx+y2cosx−y2cosx−cosy=−2sinx+y2sinx−y2

sin a =opposite\hypotenusecos a =adjacent\hypotenusetan a =opposite\adjacentcot a=adjacent\oppositesec a =hypotenuse\adjacentsec a = hypotenuse\oppositeI hope i am right and i hope it helps