The equation of tangent to the curve y=2 cos x at x=(π/4) is

Question

The equation of tangent to the curve y=2 cos x at x=(π/4) is (A) y-√2=2 √2(x-(π/4)) (B) y+√2=√2(x+(π/4)) (C) y-√2=-√2(x-(π/4)) (D) y-√2=√2(x-(π/4))

Tardigrade Admin · Accepted Answer

y=2 cos x A t x=(π/4) i j, y=(2/√2)=√2 and ( dy / dx )=-2 ⋅ sin x ∴(( dy / dx )) x -π / 4=-√2 ∴ Equation of tangent at ((π/2), √2) is y-√2=-√2(x-(π/4))

Q. The equation of tangent to the curve $y = 2 cos x$ at $x = \frac{π}{4}$ is

$y - 2 = 22 (x - \frac{π}{4})$

$y + 2 = 2 (x + \frac{π}{4})$

$y - 2 = - 2 (x - \frac{π}{4})$

$y - 2 = 2 (x - \frac{π}{4})$

$y = 2 cos x A t x = \frac{π}{4} ij, y = \frac{2}{2} = 2$
and $\frac{d y}{d x} = - 2 \cdot sin x ∴ (\frac{d y}{d x})_{x - π /4} = - 2$
$∴$ Equation of tangent at $(\frac{π}{2}, 2)$ is
$y - 2 = - 2 (x - \frac{π}{4})$

Q. The equation of tangent to the curve y=2cosx at x=4π​ is

y−2​=22​(x−4π​)

y+2​=2​(x+4π​)

y−2​=−2​(x−4π​)

y−2​=2​(x−4π​)