Final answer:
To solve the given equation, we manipulate the terms to get them in the same form and simplify the equation to determine the value of x.
Step-by-step explanation:
To solve the equation (1)/(cotx)-(secx)/(cscx)=cosx, we need to manipulate the terms to get them in the same form. First, we'll rewrite the cotangent and secant functions in terms of sine and cosine. Cotx = cosx/sinx, and secx = 1/cosx. Substituting these values, we have: (1)/(cosx/sinx)-(1/cosx)/(1/sinx) = cosx.
Next, we'll simplify the equation. Multiplying both sides of the equation by sinx*cosx, we get: sinx minus sinx = cos^3x. Simplifying further, we have: 0 = cos^3x.
From this equation, we can see that the only value of x that satisfies the equation is x = 0.