त्रिकोणमिति के सूत्र

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

 सर्वसमिकाएँ 

» 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