Question

all 11th and 12th trigonometry formulaes​

Answer 1

Answer:

for class 11 = sin(−θ)=−sinθ

cos(−θ)=cosθ

tan(−θ)=−tanθ

cosec(−θ)=−cosecθ

sec(−θ)=secθ

cot(−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

sin3A=3sinA–4sin3A=4sin(60∘−A).sinA.sin(60∘+A)

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

Trigonometry Class 12 Formulas

Definition

θ=sin−1(x)isequivalenttox=sinθ

θ=cos−1(x)isequivalenttox=cosθ

θ=tan−1(x)isequivalenttox=tanθ

Inverse Properties

sin(sin−1(x))=x

cos(cos−1(x))=x

tan(tan−1(x))=x

sin−1(sin(θ))=θ

cos−1(cos(θ))=θ

tan−1(tan(θ))=θ

Double Angle and Half Angle Formulas

sin(2x)=2sinxcosx

cos(2x)=cos2x–sin2x

tan(2x)=2tanx1–tan2x

sinx2=±1–cosx2−−−−−√

cosx2=±1+cosx2−−−−−√

tanx2=1−cosxsinx=sinx1+cosx

Answer 2

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

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

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

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

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

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

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

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

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

${ \green{ \bf{ sec θ = 1/cos θ }}}$

${ \green{ \bf{ cot θ = 1/tan θ }}}$

${ \green{ \bf{sin θ = 1/cosec θ }}}$

${ \green{ \bf{ cos θ = 1/sec θ }}}$

${ \green{ \bf{ tan θ = 1/cot θ}}}$

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

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

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

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

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

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

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

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

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

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

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