If sin x + cos x = a, then find:

(i) sin⁶ x + cos⁶ x

(ii) | sin x – cos x |

Sol (i) Write sin^6(x) + cos^6(x) as (sin^2(x))^3 + (cos^2(x))^3 and use the property [ a^3 + b^3 = (a+b)(a^2 + b^2 - ab)] and proceed ..Sol (ii) Square the given equation and find the value of sinxcosx and let |sinx - cosx| = t and square both sides now the value of sinxcosx in the obtained equation and find the value of t^2 and then t , and hence you will get the value of |sinx - cosx| Hope it helps !!