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`(1)/(2)`Solution :

`(b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2` <br> `rArr 2 sin B cos C + 2 sin C cos B + 2 sin B cos A + 2 sin B cos B = 2` <br> `rArr sin (B + C) + sin (A + B) = 1` <br> `rArr sin A + sin C = 1` <br> `rArr sin B = (1)/(2) " " ("As " 2 sin B = sin A + sin C)`Transcript

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00:00 - 00:59 | I love you won the question is in a triangle ABC if a b c are in AP and P divided by 2 + 3 by 20 and to be a + b by a sin 2A + sin to be equal to 2 then find the value of sin be here is to find the value of sin now we know when we can write a b c are in AP which means to be custom will use this latter in one more thing when it which is signed suicide release basically a by sin a equal to buy UC buy a b c are the size at ABC this a b c are the angle which is equal to 2 |

01:00 - 01:59 | s2b christava + 8 so from here we can write two into if we multiply the sunshine be with two other hand we can Crocin be single be cancelled because I see which is equals to 3 is to ask Saina 12 science will use it later we can write aur sign in to this tour this to understand the concerns from your internet sin a sin b = 2 Sin A + sin to see + c baby |

02:00 - 02:59 | and today class B by 2 + a baby send to be decreased risk capital be equal to or we can write it was great and up to our Sin B / C is to our attention and scientific and bitterness of Sin B into this and see into this will be to assign C / 12 x 12 to sign into cos B |

03:00 - 03:59 | this will be a sin b / to assign X it is to 2 sin cos A + sin b u r Sangli X into will be to Sangli into costume fancy fancy tour tour tour tour tour tour tour tour Saina can we send all the values were cancelled and will be refined to of Sin B + 2 Sin |

04:00 - 04:59 | cos B cos to Sin B cos A + 2 sin a cos b is equal to or if we take to come and then you will find that this value this value this value place value and they will be cancelled 12.2 now we can write a sin b cos theta + sin a = b this is the formula of Sin B + C + this is the formula of sin x cos a sin a cos b sin a + b is equal to this will be a aur D plus 128 triangle with no a + b + c equal to 5 therefore be places |

05:00 - 05:59 | minus plus is well you can create signup and energy = 21 when you sign up for anything it's time that you will find Sin A + sin a equal to Sin A + sin 270 we can write 2 Sin A = 21 which means we can stop One by Two digit thank you |

**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`**