Trig
posted by Katie .
Prove sin(α+β)sin(αβ)=cos^2βcos^2α

First off these are usually not this hard...just saying...ill be changing your alphas to x's and your betas to y's
we will work with the left side because it is easier.
use identity sum and difference
sin(x+y)sin(x+y)=cos^2ycos^2x
s 
(sinxcosy+cosxsiny)(sinxcosycosxsiny)=
Then, foil those and your middle two terms should cancel out leaving you with
sin^2xcos^2ycos^2xsin^2y=
now using the pythagereom theorem change all the sin^2's to cos^2 giving you
cos^2ycos^2xcos^2y[cos^2xcos^2xcos^2y]=
cos^2ycos^2xcos^2ycos^2x+cos^2xcos^2y=
cos^2ycos^2x
Respond to this Question
Similar Questions

Math
If α and β are two angles in Quadrant II such that tan α= 1/2 and tan β = 2/3, find cos(α+β) Work: cos(α+β) = [ 1  (tan α)(tan β) ] / [ 1 + (tan α)(tan β)] cos(α+β) … 
MATH
Differential equations, initial value problem. The general equation of motion is: mx"+Bx'+kx=f(t), where the independent variable is t, and the displacement x is the dependent variable. In this case, external force f(t)=0, so mx"+Bx'+kx=0 … 
Trig
prove sin(α+β)sin(αβ)=cos^2βcos^2α 
Trig
prove sin(α+β)sin(αβ)=cos^2βcos^2α 
Trig
prove sin(α+β)sin(αβ)=cos^2βcos^2α please help... this is the only one I didn't understand out of all my homework... 
Trig
Prove sin(α+β)sin(αβ)=cos^2βcos^2α 
math
Complex numbers α and β satisfy αα¯=ββ¯=−17,α+β=7i. What is the value of αβ? 
Pure Mathematics
4) The roots of the equation z^2+2z+4=0 are denoted by α and β. a) find α and β in the form re^iθ, giving the values of r and θ b) Using de Moivre's Theorem, show that α^3=β^3. c) find the exact … 
Trigonometry (identities)
1. (8cosxsinx+4cos2x)^2 +(4cosx^2+8sinxcosx)^2 2. cos(αβ)cosβsin(αβ)sinβ 3. 1+(sinxcosx)(sinx+cosx) 4. (cosβcotβ)(cosβ+cotβ) 
trigonometry
In questions 2A, 2B, and 2C below, find the exact values using the given information: sin α = 1/6 with α between 0 and π/2 sin β = 3/5 with β between π/2 and π 2A. Find cos (α + β) 2B. Find …