Posted by Candice on Friday, October 19, 2012 at 9:35am.
by equating the coefficients of sin x and cos x , or otherwise, find constants A and B satisfying the identity.
A(2sinx + cosx) + B(2cosx - sinx) = sinx + 8cosx
I got A = 2, B = 3, which the answers said were correct.
However, another part of the question asked
sinx + 8cosx
2sinx + cosx
and the answers were 2x + 3Ln (2sinx + cosx) + C
Could you explain how to get this?
Thanks in advance !!! :)
- maths - Steve, Friday, October 19, 2012 at 11:08am
use what the first part showed. Using c for cos and s for sin, you showed that
s+8c = 2(2s+c) + 3(2c-s)
= [2(2s+c) + 3(2c-s)]/(2s+c)
= 2 + 3(2c-s)/(2s+c)
now, you have ∫2 dx + ∫3du/u
2x + 3lnu
= 2x + 3ln(2s+c) + C
Answer This Question
More Related Questions
- Trig - prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= ...
- math - tanx+secx=2cosx (sinx/cosx)+ (1/cosx)=2cosx (sinx+1)/cosx =2cosx ...
- trig - express this in sinx (1/ cscx + cotx )+ (1/cscx- cotx) i got 2sinx is ...
- Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...
- Maths - Solve this equation fo rx in the interval 0<=x<=360 3sinxtanx=8 I ...
- Trig....... - I need to prove that the following is true. Thanks (2tanx /1-tan^x...
- Math - 1) evaluate without a calculator: a)sin(3.14/4) b) cos(-3(3.14)/4) c) ...
- Trig........ - I need to prove that the following is true. Thanks (cosx / 1-sinx...
- Math - Pre- Clac - Prove that each of these equations is an identity. A) (1 + ...
- maths - trigonometry - I've asked about this same question before, and someone ...