# What will be the nature of the equation sin(x + α)/sin(x + β)?

Category: QuestionsWhat will be the nature of the equation sin(x + α)/sin(x + β)?
Editor">Editor Staff asked 11 months ago

What will be the nature of the equation sin(x + α)/sin(x + β)?

(a) Possess only minimum value

(b) Possess only maximum value

(c) Does not possess a maximum or minimum value

The question was posed to me during an online exam.

The doubt is from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

Correct answer is (c) Does not possess a maximum or minimum value

The explanation: Let, y = sin(x + α)/sin(x + β)

Then,

dy/dx = [cos(x + α)sin(x + β) – sin(x + α)cos(x + β)]/sin^2(x + β)

= sin(x+β – x-α)/sin^2(x + β)

Or sin(β – α)/sin^2(x + β)

So, for minimum or maximum value of x we have,

dy/dx = 0

Or sin(β – α)/sin^2(x + β) = 0

Or sin(β – α) = 0  ……….(1)

Clearly, equation (1) is independent of x; hence, we cannot have a real value of x as root of equation (1).

Therefore, y has neither a maximum or minimum value.