Friday

October 24, 2014

October 24, 2014

Posted by **Candice** on Friday, October 19, 2012 at 9:35am.

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

hence integrate

sinx + 8cosx

-------------dx

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 11:08amuse what the first part showed. Using c for cos and s for sin, you showed that

s+8c = 2(2s+c) + 3(2c-s)

so,

(s+8c)/(2s+c)

= [2(2s+c) + 3(2c-s)]/(2s+c)

= 2 + 3(2c-s)/(2s+c)

now, you have ∫2 dx + ∫3du/u

integral is

2x + 3lnu

= 2x + 3ln(2s+c) + C

**Answer this Question**

**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 ...

maths - hey, i would really appreciate some help solving for x when: sin2x=cosx ...

Trig....... - I need to prove that the following is true. Thanks (2tanx /1-tan^x...

Math, please help - Which of the following are trigonometric identities? (Can be...

Calc II - For the following question, we need to find the length of the polar ...

Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...

Math - 1) evaluate without a calculator: a)sin(3.14/4) b) cos(-3(3.14)/4) c) ...

Math - Pre- Clac - Prove that each of these equations is an identity. A) (1 + ...