Question

give me all trigonometry formulas class 11

Answer 1

sin(−θ)=−sinθcos(−θ)=cosθtan(−θ)=−tanθcosec(−θ)=−cosecθsec(−θ)=secθcot(−θ)=−cotθ

Product to Sum Formulas

sinx siny=12[cos(x–y)−cos(x+y)]cosxcosy=12[cos(x–y)+cos(x+y)]sinxcosy=12[sin(x+y)+sin(x−y)]cosxsiny=12[sin(x+y)–sin(x−y)]

Sum to Product Formulas

sinx+siny=2sin(x+y2)cos(x−y2)sinx−siny=2cos(x+y2)sin(x−y2)cosx+cosy=2cos(x+y2)cos(x−y2)cosx−cosy=–2sin(x+y2)sin(x−y2)

Basic Formulas

sin(A+B)=sinAcosB+cosAsinB

sin(A−B)=sinAcosB–cosAsinB

cos(A+B)=cosAcosB–sinAsinB

cos(A–B)=cosAcosB+sinAsinB

tan(A+B)=tanA+tanB1–tanAtanB

tan(A–B)=tanA–tanB1+tanAtanB

cos(A+B)cos(A–B)=cos2A–sin2B=cos2B–sin2A

sin(A+B)sin(A–B)=sin2A–sin2B=cos2B–cos2A

sin2A=2sinAcosA=2tanA1+tan2A

cos2A=cosA–sin2A=1–2sin2A=2cos2A–1=1−tan2A1+tan2A

tan2A=2tanA1–tan2A

\sin 3A = 3\sin A – 4\sin^{3}A = 4\sin\left(60^{\circ}-A).\sin A .\sin\left( 60^{\circ}+A \right )

cos3A=4cos3A–3cosA=4cos(60∘−A).cosA.cos(60∘+A)

tan3A=3tanA–tan3A1−3tan2A=tan(60∘−A).tanA.tan(60∘+A)

sinA+sinB=2sinA+B2cosA−B2

Answer 2

${ \red{ \bf{ Information \: related \: to \:Trigonometry:}}}$

${ \green{ \bf{ sin θ = Perpendicular/Hypotenuse }}}$

${ \green{ \bf{ cos θ = Base/Hypotenuse }}}$

${ \green{ \bf{tan θ = Perpendicular/Base }}}$

${ \green{ \bf{sec θ = Hypotenuse/Base }}}$

${ \green{ \bf{ cosec θ = Hypotenuse/Perpendicular }}}$

${ \green{ \bf{ cot θ = Base/Perpendicular }}}$

${ \red{ \bf{Their \: reciprocal \: Identities: }}}$

${ \green{ \bf{ cosec θ = 1/sin θ }}}$

${ \green{ \bf{ sec θ = 1/cos θ }}}$

${ \green{ \bf{ cot θ = 1/tan θ }}}$

${ \green{ \bf{sin θ = 1/cosec θ }}}$

${ \green{ \bf{ cos θ = 1/sec θ }}}$

${ \green{ \bf{ tan θ = 1/cot θ}}}$

${ \red{ \bf{ Their \: co-function \: Identities: }}}$

${ \green{ \bf{ sin (90°−x) = cos x }}}$

${ \green{ \bf{cos (90°−x) = sin x }}}$

${ \green{ \bf{ tan (90°−x) = cot x }}}$

${ \green{ \bf{ cot (90°−x) = tan x }}}$

${ \green{ \bf{ sec (90°−x) = cosec x }}}$

${ \green{ \bf{ cosec (90°−x) = sec x }}}$

${ \red{ \bf{ Their \: fundamental \: trigonometric \: identities: }}}$

${ \green{ \bf{ sin²θ + cos²θ = 1 }}}$

${ \green{ \bf{ sec²θ - tan²θ = 1 }}}$

${ \green{ \bf{ cosec²θ - cot²θ = 1 }}}$