Let us consider the equation cos4⁡xa+sin4⁡xb=1a+b,x∈0,π2,a,b>0For the given equation, which of the following is correctThe value of sin2x in terms of a and b isThe value of sin8⁡xb3+cos8⁡xa3 is

We have, cos4⁡xa+sin4⁡xb=1a+b=cos2⁡x+sin2⁡xa+b⇒cos2⁡xcos2⁡xa−1a+b=sin2⁡x1a+b−sin2⁡xb⇒cos2⁡xbcos2⁡x−asin2⁡xa(a+b)a=sin2⁡xbcos2⁡x−asin2⁡xb(a+b)⇒1−sin2⁡xa=sin2⁡xb⇒Sin2x=ba+b and cos2⁡x=aa+b We have, cos4⁡xa+sin4⁡xb=1a+b=cos2⁡x+sin2⁡xa+b⇒cos2⁡xcos2⁡xa−1a+b=sin2⁡x1a+b−sin2⁡xb⇒cos2⁡xbcos2⁡x−asin2⁡xa(a+b)a=sin2⁡xbcos2⁡x−asin2⁡xb(a+b)⇒1−sin2⁡xa=sin2⁡xb⇒sin2⁡x=ba+b and cos2⁡x=aa+b  We have, cos4⁡xa+sin4⁡xb=1a+b=cos2⁡x+sin2⁡xa+b⇒cos2⁡xcos2⁡xa−1a+b=sin2⁡x1a+b−sin2⁡xb⇒cos2⁡xbcos2⁡x−asin2⁡xa(a+b)a=sin2⁡xbcos2⁡x−asin2⁡xb(a+b)⇒1−sin2⁡xa=sin2⁡xb⇒sin2⁡xb=ba+b and cos2⁡x=aa+b⇒b3+sin2⁡x3xa3=b4b3(a+b)4+a3a3(a+b)4