SOLUTION: can you help me solve this fundamental identities....please.. 1.) cosēθ(tanē θ+1)=1 2.) secē θcotē=1+cotē θ 3.)Sin θ__ =cscθ-cot θ 1+c

Algebra ->  Trigonometry-basics -> SOLUTION: can you help me solve this fundamental identities....please.. 1.) cosēθ(tanē θ+1)=1 2.) secē θcotē=1+cotē θ 3.)Sin θ__ =cscθ-cot θ 1+c      Log On


   

Question 421850: can you help me solve this fundamental identities....please..
1.) cosēθ(tanē θ+1)=1
2.) secē θcotē=1+cotē θ
3.)Sin θ__ =cscθ-cot θ
1+cos θ
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

cosēθ(tanēθ+1)=1         | (tanēθ+1)= secθē = 1/cosēθ 

cosēθ/cosēθ = 1

            1 = 1



 secēθ cotē=1+cotēθ 

 secēθcotē- cotēθ = 1

 cotēθ(secēθ - 1) = 1    | secēθ - 1 = tanēθ

 cotēθtanēθ  = 1         | tanēθ = 1/cotēθ 

 cotēθ/cotēθ = 1

           1 = 1



Sinθ/(1+cos θ) = cscθ-cot θ   |cscθ = 1/sinθ and cotθ = cosθ/sinθ

Sinθ/(1+cos θ) = (1-cosθ)/sinθ

sinēθ  = (1+cos θ)(1-cos θ)

 sinēθ = 1 - cosēθ

  sinēθ + cosēθ = 1      |pythagorean Identity