e) 2(tan x)² - 5 tan x-3 = 0 [0,2π]

Q: Solve the equation tan 3x = √3/3  on the interval [0, 2π).

A:

Q: In(√3) e dx 1+e²x A) tan-¹(3)-tan-¹(e) C) tan-¹(√3) E)-tan-¹(e)

A: Given integral: I=∫1ln3exdx1+e2x   Let, u=ex Then, dudx=ex So, exdx=du Now, the lower limit becomes:…

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

A:

Q: 16. Evaluate ft tan5 x sec¹ xdx.

A: We know that Sec²x = 1+ tan²x ∫ xn dx=( xn+1)/(n+1)

Q: T/4 (b) 4 sec (0) tan(0)dө.

A: Answer is- 4(√2-1) Explanation is given below...

Q: Wouldn't tan(x+pi)-(-sin(x)) yield tan(x+pi) + sin(x)) instead of tan(x+pi) - sin(x))?

A: Yes , there is a mistake on that question. I give u correct solution .  tan(x + π) - cos( x + (π/2))…

Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

A: