prove that cos(x-π/3)cos(x+π/3)=cos3x/4cosx
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★ Question:
prove that cos(x-π/3)cos(x+π/3)=cos3x/4cosx
★ Answer :
we know that ;
cos ( A + B) = CosA cos B - sin A sin B
and
cos ( A- B ) = CosA cos B + sin A sin B
then ,
L HS = cos(x-π/3)cos(x+π/3)
= [ cos x cos π/3 + sin X sin π / 3 ] ×
[ cos x cos π/3 - sin X sin π / 3 ]
use (A+ B ) ( A-B ) = A ² - B ²
then ,
= [cos ² x/4 - 3sin² x / 4 ]
= ( cos ² x - 3sin² x )/4
= (4cos ² x-3 )/4
now multiply and divide by cos x
= cos3x/4 cosx
= RHS
hence proved !
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