Question

If y = 2 tan x/2
prove that
Dy/dx= 2/1 + cos x

Answer 1

Step-by-step explanation:

given: y = 2tan X/2

let X/2 = z , so dz/dx = 1/2

y = 2 tanz

Dy/dx = d(2 tan z )

from the formula of d(tanx)/ dx = sec²x,

Dy/dx = 2 sec²z * dz/dx

= 2 sec² X/2 * 1/2

= sec² X/2

Dy/dx = 1/cos² X/2. ----------1

from the formula of cos 2x = 2cos²x -1

1+cos2x = 2cos²x

substitute X/2 in place of X,

1+cosx = 2 cos²x/2.

cos²x/2 = 1/2 (1+cosx) -----2

now substitute 2 in 1.

Dy/dx = 1/(1/2(1+cosx))

= 2(1+cosx)

hence proved.

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