How to solve this? lim_(x- gt;0)(tan(tanx)-tanx) (x^3) - Socratic # L = lim_(x rarr 0) (tan(tanx)-tanx) x^3 # As this is of an indeterminate form #0 0# we could directly apply L'Hôpital's rule However, to avoid some really messy trigonometry, Let us perform a substitution, #u=tanx#, then As #x rarr 0 => u rarr 0 # Thus the limit becomes: # L=lim_(u rarr 0) (tan(u)-u) (arctan^3 u)#
What is the value of tanx + cotx? | Socratic C is the correct answer You need to put on a common denominator This will be sinxcosx =(sin^2x + cos^2x) (sinxcosx) Applying the identity sin^2x + cos^2x = 1: =1 (sinxcosx) Now, recall that 1 sintheta = csctheta and 1 costheta = sectheta =cscxsecx So, C is the answer that corresponds Hopefully this helps!