Question

Ex. (O) Eliminate from given equations
x = a cot O - b cosec O
y = a cot 0 + b cosec O​

Answer 1

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Answer 2

Step-by-step explanation:

(take π = theta)

X = a cot π - b cosec π .....eq.1

Y = a cot π + b cosec π ....eq.2

add eq. 1 & 2

X + Y = a cot π - bcosec π + a cot π + b cosec π

X + Y = 2 a cot π

X + Y / 2a = cot π ......3

subtract eq. 2 & 1

Y - X = a cot π - bcosec π - a cot π + b cosec π

Y - X = 2b cosec π

Y - X / 2b = cosec π ....4

Now,

Cosec^2 π - cot^2 π = 1

so,

( Y - X /2b )^2 - ( Y + X / 2a )^2 = 1