1) To solve the equation 2sinx + cos^2x = 1, we can rewrite cos^2x as 1 - sin^2x using the Pythagorean identity for sine and cosine:
2sinx + 1 - sin^2x = 2sinx - sin^2x = 0
Now, we can factor out sinx:
sinx(2 - sinx) = 0
This equation is satisfied when sinx = 0 or 2 - sinx = 0.
When sinx = 0, x can be any multiple of π.
When 2 - sinx = 0, sinx = 2, which is not possible. Therefore, the only solution to the equation is x = nπ, where n is an integer.
2) To solve the expression tg(π/4) + sin(π/2), we first calculate the values of tangent and sine at the given angles:
tg(π/4) = sin(π/2) = 1
Now, we can substitute these values into the expression:
1 + 1 = 2
Therefore, the result of tg(π/4) + sin(π/2) is 2.
1) To solve the equation 2sinx + cos^2x = 1, we can rewrite cos^2x as 1 - sin^2x using the Pythagorean identity for sine and cosine:
2sinx + 1 - sin^2x =
2sinx - sin^2x = 0
Now, we can factor out sinx:
sinx(2 - sinx) = 0
This equation is satisfied when sinx = 0 or 2 - sinx = 0.
When sinx = 0, x can be any multiple of π.
When 2 - sinx = 0, sinx = 2, which is not possible. Therefore, the only solution to the equation is x = nπ, where n is an integer.
2) To solve the expression tg(π/4) + sin(π/2), we first calculate the values of tangent and sine at the given angles:
tg(π/4) =
sin(π/2) = 1
Now, we can substitute these values into the expression:
1 + 1 = 2
Therefore, the result of tg(π/4) + sin(π/2) is 2.