Question

Represent all the trigonometric ratios of angle A in terms of tanA

Answer 1

Express the Tan θ in terms of Tangent.
 
The Tan θ is already expressed as a tangent so:
 
Tan θ = Tan θ
 
Express the Sec θ in terms of Tangent.
 
One of the Pythagorean Identities involves only the Tan θ and the Sec θ.  That identity is:
 
Sec2 θ = 1 + Tan2 θ
 
Solve for the Sec θ by taking the square root of each side.
 
Sec θ = (1 + Tan2 θ)1/2 or
         ___________
Sec θ = √ 1 + Tan2 θ
 
 
Express the Cos θ in terms of Tangent
 
The Cos θ is the reciprocal of the Sec θ so:
 
          1          1
Cos θ = ------ = -------------
        Sec θ     √ 1 + Tan2 θ
 
 
Express the Cot θ in terms of Tangent
 
The Cot θ is the reciprocal of the Tan θ so:
 
           1
Cot θ = -------
         Tan θ
 
 
Express the Sin θ in terms of Tangent
 
The Tan θ can be expressed as:
 
         Sin θ
Tan θ = --------
         Cos θ
 
Solve the equation for the Sin θ
 
Sin θ = (Tan θ)(Cos θ)
 
Replace the Cos θ with
 
            1
Cos θ =  ------------
         √ 1 + Tan2 θ
         (Tan θ)     (1)               Tan θ
Sin θ = --------  -------------  =  -------------
           1       √ 1 + Tan2 θ      √ 1 + Tan2 θ
 
 
Express the Csc θ in terms of Tangent
 
The Csc θ is the reciprocal of the Sin θ so:
 
                               
           1       √ 1 + Tan2 θ
Csc θ = ------ = -------------
           Sin θ        Tan θ
Read more on Brainly.in - https://brainly.in/question/1499490#readmoreExpress the Tan θ in terms of Tangent.
 
The Tan θ is already expressed as a tangent so:
 
Tan θ = Tan θ
 
Express the Sec θ in terms of Tangent.
 
One of the Pythagorean Identities involves only the Tan θ and the Sec θ.  That identity is:
 
Sec2 θ = 1 + Tan2 θ
 
Solve for the Sec θ by taking the square root of each side.
 
Sec θ = (1 + Tan2 θ)1/2 or
         ___________
Sec θ = √ 1 + Tan2 θ
 
 
Express the Cos θ in terms of Tangent
 
The Cos θ is the reciprocal of the Sec θ so:
 
          1          1
Cos θ = ------ = -------------
        Sec θ     √ 1 + Tan2 θ
 
 
Express the Cot θ in terms of Tangent
 
The Cot θ is the reciprocal of the Tan θ so:
 
           1
Cot θ = -------
         Tan θ
 
 
Express the Sin θ in terms of Tangent
 
The Tan θ can be expressed as:
 
         Sin θ
Tan θ = --------
         Cos θ
 
Solve the equation for the Sin θ
 
Sin θ = (Tan θ)(Cos θ)
 
Replace the Cos θ with
 
            1
Cos θ =  ------------
         √ 1 + Tan2 θ
         (Tan θ)     (1)               Tan θ
Sin θ = --------  -------------  =  -------------
           1       √ 1 + Tan2 θ      √ 1 + Tan2 θ
 
 
Express the Csc θ in terms of Tangent
 
The Csc θ is the reciprocal of the Sin θ so:
 
                               
           1       √ 1 + Tan2 θ
Csc θ = ------ = -------------
           Sin θ        Tan θ
if u like my answer then plz mark my answer to brainlist answ plz