solve tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi

solev tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi

Expert Solution

tan2(x) = 1 , 0 ≤ x ≤ Π

tan2(x) = 1 ==> (tan(x))2 = 1

√(tan(x))2 = √1 ==> tan(x) = ± 1

Note the following: tan(x) = sin(x)/cos(x)

So, tan(x) = ± 1 ==> sin(x)/cos(x) = ± 1

Multiply both sides of the equation by cos(x):

(cos(x))·(sin(x)/cos(x)) = (cos(x))·(± 1)

sin(x) = ± cos(x)

Looking at the top half of a unit circle (where x is between 0 and Π)...

...find the coordinates where sin(x) = cos(x) and sin(x) = -cos(x)

You will see that the coordinates that match are (√2/2, √2/2), which is located at x = ∏/4, and (-√2/2, √2/2), which is located at x = 3Π/4.

Thus, x = Π/4 and x = 3Π/4

pi/4 amd 3pi/4

Nipun Maity answered 2 years ago

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