3 u maths questions (1 Viewer)

[gualtieri]

i need help for these two proving questions

prove that
1-tanxtan2x/1+tanxtan2x = 4cossqrd x-3

and

if 4tan(x-b)= 3tanx

prove that tanb=sin2x/7+cos2x

i cant seem to get the answers for both and they are taking me a while

 

[lyounamu]

i need help for these two proving questions

prove that
1-tanxtan2x/1+tanxtan2x = 4cossqrd x-3

and

if 4tan(x-b)= 3tanx

prove that tanb=sin2x/7+cos2x

i cant seem to get the answers for both and they are taking me a while

1. (1 - (tanx . 2tanx/1-tan^2(x))) / (1 + (tanx . 2tanx/1-tan^2(x))) =
((1-tan^2(x) - 2tan^x)/1-tan^2(x)) / ((1-tan^2(x) + 2tan^2(x)/1-tan^2(x)) =
1-3tan^2(x)/1+tan^2(x) = 1-3tan^2(x)/sec^2(x)
= cos^2(x) - 3sin^2(x)
= cos^2(x) - 3(1-cos^2(x))
=4cos^2(x) - 3

For q2, is it sin2x/7 + cos 2x or sin2x/(7 + cos2x)?

 

[lolokay]

i need help for these two proving questions

prove that
1-tanxtan2x/1+tanxtan2x = 4cossqrd x-3

and

if 4tan(x-b)= 3tanx

prove that tanb=sin2x/7+cos2x

i cant seem to get the answers for both and they are taking me a while

[t = tanx, c = cosx]
if you rearrange to find tanb, you get
tanb = t/(4+3t^2)
now multiply top and bottom by 2c^2
2sc/(8c^2+6s^2)
= sin2x/(2c^2 + 6(c^2+s^2))
where c^2 + s^2 = 1 and 2c^2 = cos2x + 1
= sin2x/(cos2x + 7)

 

[gualtieri]

Thanku.

 

[bored of sc]

Lyounamu and Lolokay: you guys absolutely shred at maths! Please hand me some of your superior knowledge.

 

[lyounamu]

Lyounamu and Lolokay: you guys absolutely shred at maths! Please hand me some of your superior knowledge.

nah. we are only a minor part of the maths forum in this website.