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

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places