Question

If cos A - sin A = 0, then cos⁴ A - Sin⁴ A is ___ ?

with explanation pls​

Answer 1

Answer:

cos^4 A - sin^4 A = 0

Step-by-step explanation:

cos A - sin A = 0  ---------------- (1)

(cos A - sin A)^2 = 0  {squaring on both sides}

cos^2 A + sin^2 A - 2(cos A)(sin A) = 0

cos^2 A + sin^2 A = 2(cos A)(sin A)

  1 = 2(cos A)(sin A)    {  cos^2 theta + sin^2 theta }

cos^4 A - sin^4 A = (cos^2 A - sin^2 A)(cos^2 A + sin^2 A)

                             = (cos A - sin A)(cos A + sin A)(1)

                             = (0)(cos A + sin A)        {  from (1)   }

                             = 0