Question

formulas of trigonometry​

Answer 1

Answer:

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Answer 2

Formulae of trignometry:

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

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

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

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

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

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

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

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

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

${ \green{ \bf{ sec θ = 1/cos θ }}}$

${ \green{ \bf{ cot θ = 1/tan θ }}}$

${ \green{ \bf{sin θ = 1/cosec θ }}}$

${ \green{ \bf{ cos θ = 1/sec θ }}}$

${ \green{ \bf{ tan θ = 1/cot θ}}}$

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

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

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

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

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

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

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

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

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

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

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

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

Tan (A + B) = TanA + TanB / 1 – TanA . TanB

Tan (A – B) = TanA –TanB / 1 + TanA . TanB

Sin ( A + B) . Sin (A – B) = Sin2A – Sin2B = Cos2B – Cos2A

Cos (A + B) . Cos (A – B) = Cos2A – Sin2B = Cos2B – Sin2A

Sin2A = 2 . SinA . CosA = 2 . TanA / (1 + Tan2A)

Cos2A = Cos2A – Sin2A = 1 – 2Sin2A = 2Cos2A – 1 = (1 – Tan2A) / (1 + Tan2A)

Tan2A = 2TanA / (1 – Tan2A)

Sin3A = 3 . SinA – 4 . Sin3A

Cos3A = 4 . Cos3A – 3 . CosA

Tan3A = (3TanA – Tan3A) / (1 – 3Tan2A)

SinA + SinB = 2 Sin (A + B)/2 Cos (A – B)/2

SinA – SinB = 2 Sin (A – B)/2 Cos (A + B)/2

CosA + CosB = 2 Cos(A – B)/2 Cos (A + B)/2

CosA – CosB = 2 Sin(B – A)/2 Sin (A + B)/2

TanA + TanB = Sin (A + B) / CosA . CosB

SinA CosB = Sin (A + B) + Sin (A – B)

CosA SinB = Sin (A + B) – Sin (A – B)

CosA CosB = Cos (A + B) + Cos (A – B)

SinA SinB = Cos (A – B) – Cos (A + B)