Question

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

Answer 1

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


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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.

Answer 2

Answer:

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

i.e cos x=0

Step-by-step explanation:

Given expression

$\frac{1}{cotx} -\frac{secx}{cosec x} =cosx$

We know that

$cotx =\frac{cosx}{ sinx }$

$secx=\frac{ 1}{cosx}$

$cosecx=\frac{1}{sinx}$

Put the values of cotx , secx and cosecx we get

$\frac{\frac{1}{cosx} }{sinx} -\frac{\frac{1}{cosx} }{\frac{1}{sinx} }$=cosx

By simplification we get

$\frac{sinx }{cosx} -\frac{sinx}{cosx}$=cosx

By simplification we get

cosx=0

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