त्रिकोणमिति के
सूत्र
त्रिकोणमिति अनुपातों के विशेष कोणों पर मान
Sin0° =0
Sin30° = 1/2
Sin45° = 1/√2
Sin60° = √3/2
Sin90° = 1
Cos is opposite of Sin
Tan0° = 0
Tan30° = 1/√3
Tan45° = 1
Tan60° = √3
Tan90° = ∞
Cot
is opposite of Tan
Sec0° = 1
Sec30° = 2/√3
Sec45° = √2
Sec60° = 2
Sec90° = ∞
Cosec
is opposite of Sec
2SinαCosβ=Sin(α+β)+Sin(α-β)
2CosαSinβ=Sin(α+β)-Sin(α-β)
2CosαCosβ=Cos(α+β)+Cos(α-β)
2SinαSinβ=Cos(α-β)-Cos(α+β)
Sin(α+β)=Sinα Cosβ+ Cosα Sinβ.
» Cos(α+β)=Cosα Cosβ - Sinα Sinβ.
» Sin(α-β)=SinαCosβ-CosαSinβ.
» Cos(α-β)=CosαCosβ+SinαSinβ.
» Tan(α+β)= (Tanα + Tanβ)/ (1−TanαTanβ)
» Tan(α−β)= (Tanα − Tanβ) / (1+ TanαTanβ)
» Cot(α+β)= (CotαCotβ −1) / (Cotα + Cotβ)
» Cot(α−β)= (CotαCotβ + 1) / (Cotβ− Cotα)
» Sin(α+β)=Sinα Cosβ+ Cosα Sinβ.
» Cos(α+β)=Cosα Cosβ +Sinα Sinβ.
» Sin(α-β)=SinαCosβ-CosαSinβ.
» Cos(α-β)=CosαCosβ+SinαSinβ.
» Tan(α+β)= (Tanα + Tanβ)/ (1−TanαTanβ)
» Tan(α−β)= (Tanα − Tanβ) / (1+ TanαTanβ)
» Cot(α+β)= (CotαCotβ −1) / (Cotα + Cotβ)
» Cot(α−β)= (CotαCotβ + 1) / (Cotβ− Cotα)
α/Sinα = β/Sinβ = γ/Sinγ = 2я
» α = β Cosγ + γ Cosβ
» β = α Cosγ + γ Cosα
» γ = α Cosβ + β Cosα
» Cosα = (β² + γ²− α²) / 2βγ
» Cosβ = (γ² + α²− β²) / 2γα
» Cosγ = (α² + β²− γ²) / 2γα
» Δ = αβγ/4я
» Sinθ = 0 then, θ = nπ
» Sinθ = 1 then, θ = (4n + 1)π/2
» Sinθ =−1 then, θ = (4n− 1)π/2
» Sinθ = Sinα then, θ = nπ (−1)^nα
1. Sin2α = 2SinαCosα
2. Cos2α = Cos²α − Sin²α
3. Cos2α = 2Cos²α − 1
4. Cos2α = 1 − Sin²α
5. 2Sin²α = 1 − Cos2α
6. 1 + Sin2α = (Sinα + Cosα)²
7. 1 − Sin2α = (Sinα − Cosα)²
8. Tan2α = 2Tanα / (1 − Tan²α)
9. Sin2α = 2Tanα / (1 + Tan²α)
10. Cos2α = (1 − Tan²α) / (1 + Tan²α)
11. 4Sin³α = 3Sinα − Sin3α
12. 4Cos³α = 3Cosα + Cos3α
» Sin²θ +Cos²θ =1
» Sec²θ -Tan²θ =1
» Cosec²θ -Cot²θ =1
» Sinθ =1/Cosecθ
» Cosecθ =1/Sinθ
» Cosθ =1/Secθ
» Secθ =1/Cosθ
» Tanθ =1/Cotθ
» Cotθ =1/Tanθ
» Tanθ =Sinθ /Cosθ
