Question

prove that cos to the power 4 A + sin to the power 4 - 2 cos square A into sin square A is equal to 2 cos square A minus 1 whole square​

Answer 1

Answer:

Proof is given below.

Step-by-step explanation:

$cos^{4}A + sin^{4}A - 2cos^{2}A sin^{2}A$

= $(cos^{2}A - sin^{2}A)^{2}$          (i)

(using the identity $(a-b)^2 = a^2 + b^2 - 2ab$)

Now, using the trigonometric identity $sin^{2}A + cos^{2}A = 1$, we get

$sin^{2}A = 1-cos^{2}A$          (ii)

Substituting (ii) in (i):

$(cos^{2}A - sin^{2}A)^{2}$ = $(cos^2A -(1-cos^2 A))^2$ = $(2cos^2A - 1)^{2}$

Hence proved.