X=nπ+(-1)^ny prove that

1.	X=nπ+(-1)^ny prove that
Answer» Proof: Consider the equation, sin x = sin y. Let us try to find the general solution for this trigonometric equation. sin x = sin y ⇒ sin x – sin y = 0 ⇒2cos (x + y)/2 sin (x – y)/2 = 0 ⇒cos (x + y)/2 = 0 or sin (x – y)/2 = 0 Upon taking the common solution from both the conditions, we get: x = nπ + (-1)ⁿy, where n ∈ Z

Answer»

Proof: Consider the equation, sin x = sin y. Let us try to find the general solution for this trigonometric equation.

sin x = sin y

⇒ sin x – sin y = 0

⇒2cos (x + y)/2 sin (x – y)/2 = 0

⇒cos (x + y)/2 = 0 or sin (x – y)/2 = 0

Upon taking the common solution from both the conditions, we get:

x = nπ + (-1)ⁿy, where n ∈ Z

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X=nπ+(-1)^ny prove that

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