C2 question

CKS

Given that

8tan x - 3 cos x = 0

show that

3sin^2x +8sinx -3 =0

Reply 1

elpaw

multiply by cosx, and change cos²x into (1-sin²x)

Reply 2

Newton

8tan x - 3 cos x=0

=> 8((sinx)/(cosx))-3(cosx)=0

=> cosx(8((sinx)/(cosx))-3(cosx))=0

=> 8sinx-3(cos²x)=0

By Pythagoras':

sin²x+cos²x=1

Therefore:

cos²x=1-sin²x

Therefore:

8sinx-3(1-sin²x)=0

=> 8sinx-3+3sin²x=0

Rearranging therefore gives:

3sin²x+8sinx-3=0 Q. E. D.

Newton.