Q. 1 C3.5( 2 Votes )

# Find the general

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ny, where n Z.

• cos x = cos y, implies x = 2nπ ± y, where n Z.

• tan x = tan y, implies x = nπ + y, where n Z.

Given, We know that sin x, and cosec x have negative values in the 3rd and 4th quadrant.

While giving a solution, we always try to take the least value of y

The fourth quadrant will give the least magnitude of y as we are taking an angle in a clockwise sense (i.e., negative angle)

-√2 = -cosec (π/4) = cosec (-π/4) { sin -θ = -sin θ }  If sin x = sin y ,then x = nπ + (– 1)ny , where n Z.

For above equation y = x = nπ + (-1)n ,where n ϵ Z

Or x = nπ + (-1)n+1 ,where n ϵ Z

Thus, x gives the required general solution for given trigonometric equation.

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