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00:00 - 00:59 | in equation given that the number of values of X belong in 2022 that satisfy cot x minus cos x is equals to 2 sin x ok so we are given trigonometric equations that says that Court of X cot x minus cos x is equals to twice of sin x ok first fall if it changes for every occasion into sin x sin cos x this will be cos x divided by sin x that is we have got x is equals to cos x sin x minus cosec X will be written as 1 divided by sin inverse here we have to sahi next flight taking calcium this will be equal to cos x minus 1 + sin a sin b get transferred over this will be 2 sin square x right and 2 sin square x minus 2 sin square theta minus 1 minus cos square x this will be cos x minus one will be equal to 2 into 1 minus cos square x right now |

01:00 - 01:59 | see that this is a square minus b square because a square minus b square this particular entity a square minus b square so we can write this as cos x minus one will be equal to twice into 1 + cos x into 1 minus cos x 1 - cos x right now now this is 1 - cos x will be cancelled by causes -1 -1 Subah 11:00 -1 will be equal to 2 into 1 + cos x write the value of cos a sin to find out this will be equal to minus 1 by 2 will be equal to 1 + cos x cos x will be equal to minus 1 by 2 minus one that is minus 3 by 2 value of cos x has come out to be equals to minus 3 by 2 but this first possible is but this particular value is not possible causes equals to minus 3 by 2 is not possible because cosx value lies between 1 and 9 |

02:00 - 02:59 | the value of causes lie between -1 and 1 and this is minus 3 by 2 to this particular value is not possible right so we have another condition we have another condition when cause of x minus one will be equal to zero ok so cosx will be equal to one that is this particular condition we have another condition causes -1 will be equal to zero so causes will be equal to 1 if cos x is one if cos x is 1 then sin x will be equal to zero sin x will be equal to zero is causes 12 science will be equal to zero then cortex will be equal to cot X cot X is equals to cos x by sin x cos x divided by sin x to this will be equal to cos x is one sin x is 03150 that is equals to infinity the value of cot X will be equal to infinity what is the trigonometric function to The One That Got x minus cos C content that is infinity minus something if |

03:00 - 03:59 | vinati - something is infinity because if we subtract something from infinity that will also be equal to infinity that will also come out to be equal to infinity that means from this particular value also we haven't got any solution because we have got the value of cot X that is they got the trigonometric function as equal to infinity from over here from over here we are the value of the trigonometric functions infinity and from here are the causes for smile nasiba to which is again not possible so we can state of a state that from these two values from these two values we haven't got any solution of the trigonometry question we haven't got we have not got any solution any solution of the given trigonometric function of the given string metric function ok that means that the particular trigonometric functions |

04:00 - 04:59 | 9 solutions ok that says that state of employees this as a trainer Matric function has no solutions ok because we haven't got any solution from these values of trigonometric function has no solution to see the options given in the question we see that zero that is no solution is the correct answer |

**Trigonometric equations and their solutions**

**(i) Prove that general solution of `sintheta=0` is given by `theta=npi; n in Z` (ii) Prove that general solution of `costheta=0` is `theta=((2n+1)pi/2); n in Z`**

**(iii)Prove that general solution of `tan theta=0` is `theta=npi; n in Z` (iv)Prove that the general solution of `cot theta=0` is `theta=(2n+1)pi/2, n in Z`**

**Prove that general solution of `sintheta=sin alpha` is given by `theta=npi+(-1)^n alpha, n in Z`**

**Find the general solution of the equations (i)`sin theta= sqrt3/2` (ii) `2sintheta+1=0` (iii)`cosectheta=2`**

**Prove that the general solution of `costheta=cosalpha`is given by `theta=2npipmalpha`; where `n inZ`**

**Find the general solution of the equation (i)`costheta=1/2 (ii) cos3theta=-1/2 (iii)sqrt3sec2theta=2`**

**Prove that general solution of `tan theta= tan alpha` is given by `theta=npi+alpha;n in Z`**

**Find the general solution of (i) `tan theta=1/sqrt3` (ii) `tan2theta=sqrt3` (iii)`tan3theta=-1`**

**General solution of `(i) sin^2theta = sin^2alpha; (ii) cos^2 theta = cos^2 alpha (iii) tan^2 theta = tan^2 alpha`**