Find All Solutions of Teh Equation 2sinx Root3
Solve the equation (sqrt(3))/2sinx-cosx=cos^2x
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Solution :
We have `sqrt(3) sin x = 2 (cos x + cos^(2) x)` ...(i) <br> Squaring both sides, we get <br> `3 sin^(2) x=4(cos^(2)x+cos^(4)x+2 cos^(3) x)` <br> or `3(1-cos^(2)x)=4 cos^(2)x+4 cos^(4) x+8 cos^(3) x`. <br> or `4 cos^(4) x+8 cos^(3) x+7 cos^(2) x-3 =0` <br> or `(cos x+1)(2 cos x-1) (2 cos^(2) x+3 cos x+3)=0` <br> For `cos x=-1, x=(2n+1) pi, n in Z` <br> Clearly, `cos x=-1` satisfies eq. (i). <br> Now, `cos x=1/2` <br> Clearly, for `cosx=1/2` from eq. (i), `sin x=sqrt(3)/2` <br> So, x lies in `1^(st)` quadrant. <br> `:. x=2npi +pi/3, n in Z`
Transcript
| Time | Transcript |
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| 00:00 - 00:59 | welcome without not so we have this question solve the equation root 3 by 2 sin x minus cos x is equal to cos square x so now we have this equation root 3 by 2 sin x minus cause x is equal to cos square x transposing because over there I get root 3 by 2 sin x is equal to cos square x + cos x and transpose in the to over there I get root 3 sin x is equal to 2 into cos square x + cos x sunao on acquiring port size on squaring squaring both sides I get |
| 01:00 - 01:59 | Square x is equal to 4 cos square x + cos ki power 4 x + 2 cos 2x so I can write sin square x as 1 - cos square x because I know that x square x is photo and minus cos squared so I can transform this into 3 into I am doing this because every other term in the question in the formulated equation is a cost so 1 - cos square x is equal to 4 cos square X + Cos to the power 4 x plus 8 cos cube |
| 02:00 - 02:59 | x sunao I have the contents from after solving and transposing I have caused to the power 4 x + 8 call cubic 7 call Square x minus 3 is equal to zero contract pricing on track contract pricing it I get free factors one being cause X + 1 for the bank to cause x minus one third one being 2 cos square x + 3 cos x + 3 is equal to zero so from here I get cause x is equal to -1 from here I get cause x is equal to |
| 03:00 - 03:59 | 1 by two correct so I'll be doing the factorization to for cause x is equal to -1 original equation would become x is equal to 2 and + 15 and belongs to any Integer Z so clearly cause a is equal to -1 satisfies the equation so now for cause X equal to 1 by 2 so X lies in the first quadrant correct therefore would become x is equal to 2 and 5 + 5 by 3 for all values of N belonging to integers that I hope you understood the explanation thank you |
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Find All Solutions of Teh Equation 2sinx Root3
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