Question

Solve these!!!!!!!!!!!!!!!!!!

Answer 1

1) tan13x = tan( 4x + 9x)

= { tan4x + tan9x }/{ 1- tan4x .tan9x }

tan13x ( 1- tan4x .tan9x ) = tan4x + tan9x

tan13x - tan4x.tan9x .tan13x = tan4x + tan9x

tan13x = tan4x + tan9x + tan4x.tan9x.tan13x

hence proved .


2) LHS =
cos2x.cos2y + sin²( x -y) - sin²( x + y)

= cos2x.cos2y + { sin(x -y)+sin( x -y)}{ sin(x -y) -sin(x + y)}

use formula,
sinA + sinB = 2sin(A+ B)/2.cos( A-B)/2
sinA - sinB = 2sin(A-B)/2 .cos(A+B)/2


= cos2x.cos2y + { 2sin( x-y+x+y)/2.cos(x-y-x-y)}{ 2sin(x-y-x-y)/2.cos(x-y+x+y)/2}

=cos2x.cos2y + { 2sinx.cos(-y)}{2sin(-y).cosx }

= cos2x.cos2y - { 2sinx.cosx}{2siny.cosy}

=cos2x.cos2y - { sin2x }{sin2y}

=cos2x.cos2y - sin2x.sin2y

=cos( 2x +2y) = RHS

Answer 2

Answer is in the pic......