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

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shankvee\Best ResponseYou've already chosen the best response.2
Ok 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?
 2 years ago

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

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

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

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

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

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

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

Hannah_AhnBest ResponseYou've already chosen the best response.0
4sin^2xcos^2 = 2sin2x^2 not sin2x^2 ?
 2 years ago

shankvee\Best ResponseYou've already chosen the best response.2
no 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
 2 years ago

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

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

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

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

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

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

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

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

Hannah_AhnBest ResponseYou've already chosen the best response.0
isn't it pythagorean indentities
 2 years ago

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

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

shankvee\Best ResponseYou've already chosen the best response.2
You 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
 2 years ago

shankvee\Best ResponseYou've already chosen the best response.2
even 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...
 2 years ago

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

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

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

shankvee\Best ResponseYou've already chosen the best response.2
I'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
 2 years ago

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

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

shankvee\Best ResponseYou've already chosen the best response.2
So 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....
 2 years ago

shankvee\Best ResponseYou've already chosen the best response.2
Any 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.
 2 years ago

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

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

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

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

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

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

Hannah_AhnBest ResponseYou've already chosen the best response.0
i learned it i will need to review it
 2 years ago

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