Someone please help! trig identities. show work too bc i don’t understand

120/169

Step-by-step explanation:

one could use a calculator to find the inverse sine of 5/13 = 22.61986494804042617294901087668...° then double it and take the sine to get 0.71005917159763313609467455621302...

OR

cosθ = √(1 - sin²θ) = √(1 - 25/169) = √(144/169) = 12/13

then use the double angle identity

sin(2θ) = 2sinθcosθ = 2(5/13)(12/13) = 120/169

which is approximated by our calculator result.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18