If cos^{^{^⁴}}A – sin^{^{^⁴}}A = x, then the value of x is ;

2cos^{^{^²}}A – 1

2cos^{^{^²}}A + 1

cos^{^{^²}}A – 1

cos^{^{^²}}A + 1

Answer : Option A

Explanation :

x = cos^{^{^⁴}}A – sin^{^{^⁴}}A

= (cos^{^{^²}}A + sin^{^{^²}}A) (cos^{^{^²}}A – sin^{^{^²}}A)

= cos^{^{^²}}A – sin^{^{^²}}A = cos^{^{^²}}A – (1 – cos^{^{^²}}A)

= 2cos^{^{^²}}A – 1

sin^{^{^²}}A + cos^{^{^²}}A = 1

If cos4A – sin4A = x, then the value of x is ;