A community for students.
Here's the question you clicked on:
 0 viewing
Hannah_Ahn
 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)
Hannah_Ahn
 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)

This Question is Closed

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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.