Question

If cosec 0 + cot 0 =p, then prove that cos 0 = ( p^2 -1) / (p²+1)​

Answer 1

Given:

Cosec 0 + Cot 0 = p ——> 1

We know that

Cosec^20 - Cot^20 = 1

(Cosec 0 + Cot 0)*(Cosec 0 - Cot 0) = 1

p*(Cosec 0 - Cot 0) = 1 [From 1]

Cosec 0 - Cot 0 = 1/p ——> 2

Adding Equations 1 & 2,

(Cosec 0 + Cot 0) + (Cosec 0 - Cot 0) = p + (1/p)

2Cosec 0 = (p^2 + 1)/p ——> 3

Subtracting Equations 1 & 2,

(Cosec 0 + Cot 0) - (Cosec 0 - Cot 0) = p - (1/p)

Cosec 0 + Cot 0 - Cosec 0 + Cot 0 = p - (1/p)

2Cot 0 = (p^2 - 1)/p ——> 4

Divide 4 by 3,

2Cot 0 (p^2 - 1)/p
———- = —————
2Cosec 0 (p^2 + 1)/p


Cot 0 (p^2 - 1)
———- = ————
Cosec 0 (p^2 + 1)

Cos 0 * Sin 0 (p^2 - 1)
——————— = —————
Sin 0 (p^2 + 1)

Cos 0 = (p^2 - 1)/(p^2 1)

Hence Proved

Answer 2

Answer:

proved......

Step-by-step explanation:

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