Question

If x = `a[cosθ + logtan  θ/2]`, y = asinθ then `(dy)/(dx)` = ______.

Options

• cosθ

• sinθ

• tanθ

• cosecθ

Answer 1

If x = `a[cosθ + logtan  θ/2]`, y = asinθ then `(dy)/(dx)` = tanθ.

Explanation:

`(dy)/(dx) = (acosθ)/(-asinθ + (asec^2  θ/2)/(tan  θ/2) xx 1/2)`

= `(acosθ)/(-asinθ + a/(2cos  θ/2 sin  θ/2)`

= `(acosθ)/(a/sinθ - asinθ)`

= `(acosθsinθ)/(a - asin^2θ)`

= `(cosθsinθ)/(cos^2θ)`

= tanθ