Relation among sinθ, cosθ, tanθ aur cotθ

                  Trigonometry - 8   

Hello friends! Humane last two post me trigonometric ratio ke square
 and reciprocal relations ke baare me jaana tha. Issi topic ko aage badate huye aaj hum Relation among sinθ , cosθ , tanθ and cotθ ke baare me jaanege.

Matalab aaj hum jaanege ki , sin θ, cos θ, tan θ aur cot θ me kya relations hai ? Ye relation bhi last two relation ki tarah bahut important hai. Iss article me hum iss relation ke baare me completly jaanege. Aayiye aaj ka topic start karte hai.

Relation among sin θ, cos θ, tan θ and cot θ

Inn 4th trigonometric ratio ke beech main 2 relations hai. Jo iss prakar se niche diya gaya hai.

1.     tan θ = sin θ/cos θ

2.     cot θ = cos θ/sin θ

Ab hum inn relations me se ek relation ko derived ( nigaman ) karenge. 

Aayiye (1) wala derived karte hai.

Suppose karte ki , humare paas ek Right angle triangle ∆ABC hai. Jisme /_BAC = θ aur /_ABC = 90°

Figure-2

Ab figure-2 ki help se -: Hum jaante hai ki ,
• sin θ = BC/AC    ........(i)
• cos θ = AB/AC   ........(ii)
• tan θ = BC/AB   ........(iii)
Eq(i) ko (ii) se divide kariye.

           sin θ   =   BC/AC  
          cos θ        AB/AC

                       = BC/AB

           sin θ   =   BC   
          cos θ         AB

           sin θ   =  tan θ
          cos θ                          [ from(iii) ]

⇒   tan θ = sin θ/cos θ

To iss prakar se hum (1) relation ko derived kar sakte hai.

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Second (2) relation ko bhi issi tarah se derived kiya jaa sakta hai. Mai reciprocal relation ka use kark (2) relation ko derived karunga.
Aayiye isse bhi shikh lete hai.

Hum jaante hai ki ,
                      cot θ = 1/tan θ

aur  tan θ = sin θ/cos θ
So,
                      cot θ = 1/ (sin θ/cos θ)
Or                 cot θ = cos θ/sin θ

⇒  cot θ = cos θ/sin θ

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