Question

If y = [(sin2x)/(1 – cotx)] + [(cos2x)/(1 – tanx)] and |[dy/dx]|x=(π/4) =_____

(a) 0

(b) + 1

(c) (1/2)

(d) |(1/2)|

Answer 1

The correct option (a) 0

Explanation:

y = [(sin2x)/(1 – cotx)] + [(cos2x)/(1 – tanx)]

= [(sin2x)/(1 – {(cosx)/(sinx)})] + [(cos2x)/(1 – {(sinx)/(cosx)})]

= [(sin3x)/(sinx – cosx)] – [(cos3x)/(sinx – cosx)]

∴ y = sin2x + cos2x + sinxcosx

∴ y = 1 + [(sin2x)/2]

(dy/dx) = (1/2) × cos2x (2)

∴ (dy/dx) = cos2x

∴ |(dy/dx)|x=(π/4) = cos(π/2)

= 0