How do you prove : sin^4a+2cos^2a-cos^4a=1 ? ?

to prove that sin⁴a+2cos²a-cos⁴a, we can factor out cos²a

sin⁴a+2cos²a-cos⁴a

= sin⁴a+cos²a(2-cos²a)

since sin²a + cos²a = 1, cos²a = 1 - sin²a so substituting

= sin⁴a+cos²a(2-(1 - sin²a) )

= sin⁴a+cos²a(1 + sin²a)

= sin⁴a+cos²a+ sin²a cos²a distribution

= sin⁴a + sin²a cos²a +cos²a

= sin²a(sin²a+cos²a) +cos²a by factoring

= sin²a * 1 + cos²a by pythagorean identity

= 1 by pythagorean identity

step-by-step explanation:

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.