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 3 years ago
solve algebraically for x:
4sin^2x=3tan^21
(answers: x=pi over 4, 3pi over 4, 5pi over 4, and 7pi over 4)
 3 years ago
solve algebraically for x: 4sin^2x=3tan^21 (answers: x=pi over 4, 3pi over 4, 5pi over 4, and 7pi over 4)

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shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Ok this you can do, Just juggle about with identites first multiply both sides by cos ^2 x, LHS becomes 4sin^2 x cos ^2 x=(sin 2x)^2. Did you understand how?

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Did you understand till here lets go step by step.

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0shouldn't it be 2sin1/2^2

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Do you know the identity 2sinx cosx=sin2x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2good so you have here 2sinx cos x the whole squared which is sin 2x the whole squared.

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2So On the LHS there is sin ^2 2x which we can write it as 1 cos ^2 2x

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0shouldn't it be 2sin^2 2x??

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2no do it agian 2 wont come.

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.04sin^2xcos^2 = 2sin2x^2 not sin2x^2 ?

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2no it is square in this one 2sinx cos x becomes sin 2x and another 2sinx cos x becomes sin 2x you need two 2's to make (sin x cosx)^2 (sin 2x)^2

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0OHHH!!!! I didn't know that .. :P thanks, let's keep it going

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2So yeah write sin ^2 2x as 1 cos ^2 2x. ok?

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Ok so now come to RHS 3tan ^2 x * cos^2 x  cos ^2 x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2tan ^2 x *cos ^2 x=sin^2 x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2so RHS becomes 3sin^2 x  cos^2 x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Now do you know the identities sin ^2 x=(1cos2x)/2 and cos ^2 x=(1+cos 2x)/2

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0i don't know abhout the /2

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2no no that identity is \[\sin ^{2}x=(1\cos 2x)/2\]

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0isn't it pythagorean indentities

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2ITS \[\cos 2x \] not\[\cos ^{2}x\]

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0i am so sorry. :S i didn't cover that identities yet

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2You have to use those identities you have 1 cos ^2 2x on the LHS so write everything in the RHS in terms of cos 2x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2even if you didn't know them now you know them... so substitue for sin ^2 x and cos ^2 x by using the identities i told you and tell me what you get...

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2did you get what i'm trying to tell?

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Good so tell me what do you have on the RHS...

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0unfortunately, i cannot work it out with these identities that i didn't learn for a test. .

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2I'm sorry i don't know how to solve the problem in any other way.... Anyway if you want to continue with my method take LCM and all and simplify both sides you get cos ^2 2x=2cos 2x ths means cos 2x=0 and cos 2x=2(This case is not possible so the answer is just cos 2x=0

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0it's okay I still appreciate you for what you've done. :)

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Okay here's an alterative easier solution , You can use sec ^2 x= 1+tan ^2 x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2So in the RHS write tan ^2 x as sec ^2 x 1 and simplify you get 84cos^2 x= 3sec^2 x. See if you understand till here....

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Any doubts in what i have done? If not let us say cos^2 x is some t then obviously sec ^2 x=1/cos^2 x=1/t so you get 84t=3/t. 8t4t^2=3. 4t^28t+3=0 this implies t=1/2 or t=3/2 t=3/2 is not possible hence t=1/2 or cos ^2 x=1/2 whose obvious solutions are pi/4,3pi/4 and so on.

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2lalaly wrong the equation when divided as by you becomes 4=3/cos^2x  cosec^2x

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2did you get it hannah?

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0sorry i took a break . i am keep looking to figure out what you have done .

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0i feel like you are one of my tutor that i had in my past years :) haha he was great. anyway ..

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2What a compliment \m/

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Do you know how to solve quadratic equations?

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0i learned it i will need to review it

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.2Anyway read what i have done properly its not too hard to understand i've just substitued tan^2 x as sec ^2 x 1
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