Question

if y = sinx and z =cosx ,then dy/dz is equal to :
a) -cosecx cosx
b) π/180cosecπx/180 cosx
c) -π/180cosecx cosπx/180
d) None of the above​

Answer 1

Answer:

(A) -cosecx•cosx

Hint:

Use chain rule and simplify dy/dz

For solution, refer attachement !!

Hope this answer helped you ✌

Answer 2

Answer:

a) -cosecx•cosx

Solution:

• GIVEN : y = sinx , z = cosx
• TO FIND : dy/dz = ?

We have ;

y = sinx

Differentiating both sides wrt x , we get ;

=> dy/dx = d(sinx)/dx

=> dy/dx = cosx ------(1)

Also,

z = cosx

Differentiating both sides wrt x , we get ;

=> dz/dx = d(cosx)/dx

=> dz/dx = -sinx ---------(2)

Now,

=> dy/dz = (dy/dx) / (dz/dx)

=> dy/dz = cosx / (-sinx) {using eq-(1),(2)}

=> dy/dz = - (1/sinx)•cosx {cosecx=1/sinx}

=> dy/dz = - cosecx•cosx

Hence,

dy/dz = - cosecx•cosx