How do you prove cos(u-v)/(cosusinv)=tanu+cotv?
1 Answer
see explanation
Explanation:
Attempt to convert the left side into the form of the right side.
Consider the numerator of the function on the left. Using the appropriate
color(blue)"addition formula"
color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(cos(A-B)=cosAcosB+sinAsinB)color(white)(a/a)|)))
rArrcos(u-v)=cosucosv+sinusinv We now have :
(cosucosv+sinusinv)/(cosusinv) now divide the terms on the numerator by the denominator.
rArr(cancel(cosu)cosv)/(cancel(cosu)sinv)+(sinucancel(sinv))/(cosucancel(sinv))=(cosv)/(sinv)+(sinu)/(cosu)
color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(tantheta=(sintheta)/(costheta)" and " cottheta=(costheta)/(sintheta))color(white)(a/a)|)))
rArr(cosv)/(sinv)+(sinu)/(cosu)=cotv+tanu=tanu+cotv Thus left side = right side
rArr" proven"
