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maximum value of ` f(theta ) AA theta in R ` is ` (1)/(4) ` maximum value of ` f(theta) AA theta in R ` is ` (1)/(8) ` ` f(0)= (1)/(8) ` Number of principle solutions of ` f(theta) = 0 ` is 8

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00:00 - 00:59 | in this question let St tabhi equal to this function given function and then we have to check which of the following options about the given function as through the first of all latest simplify the given function so we have if theta is equal to cos theta minus Cos pi by 8 into cos theta minus Cos 3 pi by 8 and we have latest single function we have cos 55 B and Cos 75 B 255 B can be written as 5 minus 5 by some writing that I am writing cost theta and I am writing cause of 558 is caused by - 3 pi by because this is equal to pi by and the last expression is cos theta minus Cos 75 B that can be written as 5 minus 5 by 8 this is the ft now be no cause of Pi minus theta is equal to minus cos |

01:00 - 01:59 | theta minus Alpha is equal to minus cos alpha this would become positive here and it will also become positive so we have three tier is equal to cos theta minus Cos pi by 8 into cos theta minus Cos 3 pi by 8 real having cos theta + cos 3 pi by 8 and Cos theta + Cos pi by 8 now this is a minus b a + b a minus b a + b is equal to a square minus b square using that identity would be equal to a minus b + b cos square theta minus cos square pi by and here we are having cos square theta minus Cos 3 pi by now we know one thing Sin |

02:00 - 02:59 | of 90 minus theta pi by 2 minus theta is equal to cos theta this we know similarly 358 free fire by it can be written as Sin of 5 by 2 minus 5 by 3 5 by 8 very common and this is equal to sign off aur pi by 8 - 35 by that is pi by 2 cos of 35 b is equal to sin pi by today substitute that here so will be having f l is equal to cos square theta minus cos square pi by 8 into cos square theta minus sin square pi by 8 this is the expression now will multiply both the brackets x x l would be equal to cos square |

03:00 - 03:59 | theta into cos square theta is Cos raise to the power 4 theta cos square theta into this would be minus cos square theta sin square pi by 8 and if x is to will get minus cos square theta cos square pi by 8 and minus cos square pi by 8 into minus sin square pi by that would be sin square pi by 8 into cos square pi by 8 this is the value of the expression now we can take cos square theta common from these two terms f l would be equal to Cos raise to the power 4 theta minus cos square theta in the bracket we have sin square pi by 8 + cos square pi by 8 and here it is multiply and divide the expression by 4 1 by 4 and twice of sin pi by 8 Cos pi by 8 whole square |

04:00 - 04:59 | open the bracket B grade 4 / 4 that will thus be same as above expression sin square theta + cos square theta is equal to 1 and also to sin alpha cos alpha is always equal to sign twice of Alpha using this identity here and sin square theta + cos square theta is equal to 1 so we have a theta is equal to Cos raise to the power 4 theta minus only cos square theta will be there and + 1 by 4 this can be written as 2 sin theta cos theta into sin alpha Cos A can be written as sin 12 let me sign of twice of fire by does that mean if I buy now latest cos square theta common from this hotel cos squared theta minus one a sin pi by 4 is 1 by root 2 cos 1 - |

05:00 - 05:59 | cos square x minus sin square sin square theta minus cos square theta minus 1 minus of sin square theta into this cos square theta + that would become one by one by 4 into one by two is 1 by 8 now if you would be equal to again multiply and divide it is this equation by 4 so we are left with minus 1 by 4 we get price of sin theta cos theta whole square that means sin 2 theta + 1 by now let us take 1 by 8 common so we're left with 1 - 2 sin square Peter and Binu an identity that sin square of 2 theta is always equal to 1 minus Cos 1 - cos theta sin square theta is equal to 10 science 2 sin square theta is equal to 1 minus Cos 2 theta |

06:00 - 06:59 | this is an identity so we can write here it is x 2 theta 2 science 2 sin square theta would be equal to 1 minus Cos 4 theta to be have yas theta is equal to 1 by 8 1 - 1 + cos 4 theta would be equal to cos 4 theta divided by this is the value of the given FC now latest on taking the option the first option says maximum value so cos theta always belong to -121 so the maximum value of f theta would also always be when cos theta is equal to 1 and it would be won by the maximum value of cos theta is 1 by and also f of zero ok 0 to I am writing f of zero |

07:00 - 07:59 | would be equal to cos 0 by 80 is 1 a 40 is 1 by 8 antiepileptic f m is equal to zero the number of principal solution for f theta is equal to zero that means cos 4 theta by 8 is equal to zero this implies 4 theta should be equal to zero to from here we can say 4 theta should be and should be equal to 1 + 1 by 2 one or multiple of 5 by 2 cm find the principal value so between minus 5 by 4 theta belonging to minus 525 we have the values of theta is equal to minus 7 5 by 8 6 4 theta is equal to sin theta would be equal to 2 and + 1 by 25 by 82 - 758 - 558 - 35 by 8 and plus |

08:00 - 08:59 | minus I should write plus minus plus minus and also plus minus 5 by these are the values of theta between minus 5 by which are satisfying this condition that means the number of values of principal solutions are 12345678 solutions are there the correct options would be superstar fall we have seen the maximum value of theta is 1 by 8 option would be correct as 0 is 1 by 8 option would be correct in number of principal solutions of 1 litre is equal to zero is it is also a b c d |

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