Question

Given 1/cotx - secx/cscx = cosx find a numerical value of one trigonometric function of x.

Answer 1

The numerical value of one trigonometric function of x is zero.

i.e cos x=0

Explanation:

Given expression

`(1)/(cotx) -(secx)/(cosec x) =cosx`

We know that

`cotx =(cosx)/( sinx )`

`secx=( 1)/(cosx)`

`cosecx=(1)/(sinx)`

Put the values of cotx , secx and cosecx we get

`((1)/(cosx) )/(sinx) -((1)/(cosx) )/((1)/(sinx) )`=cosx

By simplification we get

`(sinx )/(cosx) -(sinx)/(cosx)`=cosx

By simplification we get

cosx=0

Hence, option c. cosx=0 is the correct answer.

Answer 2

The expression on the left simplifies to
tan(x) - sin(x)/cos(x) = 0

So, your expression is 0 = cos(x). This matches your answer choices ...
c. cos(x) = 0


_____
Of course, at cos(x)=0, the entire left side of the equation amounts to 1/0 - 1/0, so is undefined. Effectively, there is no solution.