(cos2x/cosx)+(cosx/cos2x)=1

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To solve this equation, we can first simplify the left side by finding a common denominator:

(cos^2x/cosx) + (cosx/cos^2x)
= [(cos^2x)^2 + cosx^2] / (cosx * cos^2x)
= (cos^4x + cos^2x) / (cosx^3)

Now, we can simplify further by factoring out a cos^2x from the numerator:

= cos^2x(cos^2x + 1) / (cosx^3)
= cos^2x(cos^2x + 1) / (cosx * cos^2x)
= (cos^2x + 1) / cosx

Therefore, the equation cos^2x + 1 = cosx holds true, and the given equation simplifies to 1 = 1.