Question

sin2x = cos(3x -10), find tanx

Answer 1

tried using cos(3x) = 4cos^3 x - 3cosx and sin(3x) = 3sinx - 4sin^3x
but the cos10 and sin10 really messed things up.
So how about Newton's method?

let y = sin2x - cos(3x - 10)
dy/dx = 2cos2x + 3sin(3x-10)
looking at the graph:
https://www.wolframalpha.com/input/?i=solve++sin2x%3D++cos%283x+-10%29
let's start with x = 1
newx = x - (sin2x - cos(3x-10)) / (2cos2x + 3sin(3x -10)
and using a "good calculator" with memory storage ....
start with a guess of x = 1
x -- newx
1 1.055433864
1.055433864 __ 1.051890393
1.051890393 ___ 1.05749655
1.05749655 ___ 1.057522203
1.057522203 ___ 1.057522204 <---- correct to 8 decimal places

looks like another solution near x = 2
x -- newx
2 2.107109029
2.107109029 ___ 2.101660281
2.101660281 ___ 2.095289164
2.095289164 ___ 2.13728505
2.13728505 ___ 2.145633424
2.145633424 __ 2.146017541
2.146017541 ___ 2.146018366
one more step should do it correct to 8 decimals

get as many solutions as you want

Answer 2

sin2x = cos(3x-10degree), find tanx, significant figures

Answer 3

You didn't say you wanted the units were in degrees,
unless otherwise stated, at this level we work in radians.

My derivative is only valid in radians.
Wolfram's graph assumes the 10 is in radians

so you will have to change the 10° to radians, use (3x-π/18)
repeat the above iteration, change the answer back to degrees,
then take the tan of the x

good luck.

Answer 4

sin= 90 - (3x -10)
2x = 90 -3x + 10
2x =100 -3x
2x + 3x = 100 - 3x + 3x
5x = 100
5x/5 = 100/5
x = 20
tanx sin/cos
tanx = sin40/cos50