If $$cos$$⁡α$$+$$$$cos$$⁡β$$=0=$$$$sin$$⁡α$$+$$$$sin$$⁡β then $$cos$$⁡$$2$$α$$+$$$$cos$$⁡$$2$$β is equal to

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If $$cos$$⁡α$$+$$$$cos$$⁡β$$=0=$$$$sin$$⁡α$$+$$$$sin$$⁡β then $$cos$$⁡$$2$$α$$+$$$$cos$$⁡$$2$$β is equal to

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Given $$cos$$⁡α$$+$$$$cos$$⁡β$$=0$$ and $$sin$$⁡α$$+$$$$sin$$⁡β$$=0On$$ squaring and subtracting both the equations, we get $$($$$$cos$$⁡α$$+$$$$cos$$⁡β$$)2$$−$$($$$$sin$$⁡α$$+$$$$sin$$⁡β$$)2=0$$⇒$$cos2$$⁡α$$+cos2$$⁡β$$+2cos$$⁡α$$cos$$⁡β−$$sin2$$⁡α$$+sin2$$⁡β$$+2sin$$⁡α$$sin$$⁡β$$=0$$⇒$$cos2$$⁡α−$$sin2$$⁡α$$+cos2$$⁡β−$$sin2$$⁡β$$+2$$[$$cos$$⁡α$$cos$$⁡β−$$sin$$⁡α$$sin$$⁡β]$$=0$$⇒$$cos$$⁡$$2$$α$$+$$$$cos$$⁡$$2$$β$$+2cos$$⁡$$($$α$$+$$β$$)=0$$⇒$$cos$$⁡$$2$$α$$+$$$$cos$$⁡$$2$$β$$=$$−$$2cos$$⁡$$($$α$$+$$β$$)$$

If $\cos α + \cos β = 0 = \sin α + \sin β$ then $\cos 2 α + \cos 2 β$ is equal to

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If cos⁡α+cos⁡β=0=sin⁡α+sin⁡β then cos⁡2α+cos⁡2β is equal to

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If $\cos α + \cos β = 0 = \sin α + \sin β$ then $\cos 2 α + \cos 2 β$ is equal to