How do you apply the sum and difference formula to solve trigonometric equations?
1 Answer
Main Sum and Differences Trigonometric Identities
#cos (a - b) = cos a*cos b + sin a*sin b#
#cos (a + b) = cos a*cos b - sin a*sin b#
#sin (a - b) = sin a*cos b - sin b*cos a#
#sin (a + b) = sin a*cos b + sin b*cos a#
#tan (a - b) = (tan a - tan b)/(1 + tan a*tan b)#
#tan (a + b) = (tan a + tan b)/(1 -tan a*tan b)#
Application of Sum and Differences Trigonometric Identities
Example 1: Find
#sin 2a#
#= sin (a + a)#
#= sin a*cos a + sin a*cos a#
#= 2*sin a*cos a#
Example 2: Find
#cos 2a#
#= cos (a + a)#
#= cos a*cos a - sin a*sin a#
#= cos^2 a - sin^2 a#
Example 3: Find
#cos ((13pi)/12)#
#= cos (pi/3 + (3pi)/4)#
#= cos (pi/3)*cos ((3pi)/4) - sin (pi/3)*sin ((3pi)/4)#
#= -(sqrt2)/4 - (sqrt6)/4#
#= -[sqrt2 + sqrt6]/4#
