Question

Find y. cosec(π/2+x) + y cos x cot (π/2+x) = sin(π/2 + x)​

Answer 1

Given: The expression  cosec(π/2+x) + y cos x cot (π/2+x) = sin(π/2 + x)​

To find: The value of y.

Solution:

• Now we have given cosec(π/2+x) + y cos x cot (π/2+x) = sin(π/2 + x)​

• We know :

              cosec (π/2+x) = sec x

              cot (π/2+x) = - tan x

              sin(π/2 + x)​ = cos x

• So substituting this, we get:

              sec x + y cos x (- tan x) = cos x

              sec x + y cos x (- sin x / cos x) = cos x

              sec x - y sin x = cos x

              sec x - cos x = y sin x

              1/cos x - cos x = y sin x

              1 - cos^2 x = y sin x cos x

              sin^2 x = y sin x cos x

              sin x = y cos x

              y = sin x / cos x

              y = tan x

Answer:

           So the value of y is tan x.