To solve this equation, we will first rewrite ctgx as 1/tgx and expand the left side using trigonometric identities:
cosx * (1/tgx) - sinx = cos2cosx/tgx - sinx = cos2x
Next, we will replace tgx with sinx/cosx to simplify the equation:
cosx/(sinx/cosx) - sinx = cos2cos^2(x)/sinx - sinx = cos2x
Now, we will multiply both sides by sinx to eliminate the denominator:
cos^2(x) - sin^2(x) = sinx*cos2x
Using the Pythagorean identity cos^2(x) - sin^2(x) = cos(2x), the equation becomes:
cos(2x) = sinx*cos2x
Therefore, cosx ctgx - sinx = cos2x is equivalent to cos(2x) = sinxcos2x.
To solve this equation, we will first rewrite ctgx as 1/tgx and expand the left side using trigonometric identities:
cosx * (1/tgx) - sinx = cos2
cosx/tgx - sinx = cos2x
Next, we will replace tgx with sinx/cosx to simplify the equation:
cosx/(sinx/cosx) - sinx = cos2
cos^2(x)/sinx - sinx = cos2x
Now, we will multiply both sides by sinx to eliminate the denominator:
cos^2(x) - sin^2(x) = sinx*cos2x
Using the Pythagorean identity cos^2(x) - sin^2(x) = cos(2x), the equation becomes:
cos(2x) = sinx*cos2x
Therefore, cosx ctgx - sinx = cos2x is equivalent to cos(2x) = sinxcos2x.