SOLUTION: if {{{COS(A+B)*SIN(C+D)}}}{{{"="}}}{{{COS(A-B)*SIN(C-D)}}},SHOW THAT {{{COT(A)*COT(B)*COT(C)}}}{{{"="}}}{{{COT(D)}}}

SOLUTION: if {{{COS(A+B)SIN(C+D)}}}{{{"="}}}{{{COS(A-B)SIN(C-D)}}},SHOW THAT {{{COT(A)COT(B)COT(C)}}}{{{"="}}}{{{COT(D)}}}

Question 321758: if ,SHOW THAT
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Using well known formulas:



Using "FOIL" on both sides:







(Notice that it took two lines to write that equation because it was so long!
The left side, then the equal sign, then the right side.)

The first terms on each side are the same, so they cancel.
The last terms on each side are also the same so they cancel:







So all we have left is this:



Add the opposites of both negative terms to both sides and we end up with:



Divide both sides by 2



Divide both sides by ,



Cancel what will cancel:





Regroup the factors on the left:



Use the identity  and you end up
with




Edwin

RELATED QUESTIONS
cos2x-cos4x/sin2x+sin4x= a. cot x b. tan x c. sin x d. cos... (answered by Solver92311)

cos2x-cos4x -------------- = sin2x+sin4x a. cot x b. tan x c. sin x d. cos... (answered by math_helper)

cos2x+cos4x -------------- = sin2x-sin4x a. cot x b.-cot x c. sin x d.- tan x (answered by MathLover1,ikleyn)

cos^2theta sectheta= A. tan theta B. cot theta C. sin theta D. cos theta E. csc theta... (answered by texttutoring)

The expression sin θ (cot θ - csc θ) is equivalent to? A) 2 Cos θ (answered by stanbon,lynnlo)

The simplified form of tan0/cot 0 is; a. 1 b. (tan 0)^2 c. (cot 0)^2 d. (sin 0)(cos... (answered by eperette)

Evaluate the expression. {{{ cos(-x) }}}{{{ cot(x) }}}{{{ sin(-x) }}} A.) {{{ cos(x)... (answered by Edwin McCravy)

Show that (a) (sec^4-1)/(tan^2x) =2tan^2x (b) (cosec^4x -1)/(cot^2x) =2+cot^2x (c)... (answered by Edwin McCravy,MathTherapy)

How would this expression look evaluated? {{{ cos(-x) }}}{{{cot(x)}}}{{{sin(-x) }}}... (answered by Alan3354)