Mth 102 Assignment no.2 solution fall 2021
Assignment No. 2 of MTH 102Question No.1:If = 17, =37, find the first term, common difference and .Solution:Given Data:=17=37Find outFirst term=Common difference= d6th term=Formula:So,= 17=And= =3737=Subtracting equation (i) from equation (ii)We get,20= 4dd= 20/4d=5So the common difference is 5. Putting d=5 in equation .1We get17= 17=So the first term is -3.From above formula we can find 6th termSo,So the 6th term is 22.Question no. 2:Find the value of sin 105 )Solution:=sin 105 =sin (60According to formula=sin 60 45 + cos 60 sin 45/2, sin45 =1/ , cos 45 1/ , cos 60 1/2= /2× 1/ + 1/2× 1/= /2 +1/2=Question no. 3: Show that Solution:L.H.S. =Formula:∴ Sin (A+B) = sin A cos B+ cos A sin B and cos (A+B) = cos A cos B - sin A sin BSo,L.H.S. = (sinϴ cosπ/6 +cosϴ sin π/6) + (cosϴ cosπ/3 - sinϴ sinπ/3) ∴ sinπ/6 =1/2, cos π/6= /2, cos π/3= 1/2, sin π/3= /2Now putting above values, we get= (sinϴ /2 +cosϴ1/2) + (cosϴ1/2 - sinϴ /2)=sinϴ /2 + cosϴ1/2 +cosϴ1/2 -sinϴ /2= cosϴ1/2 + cosϴ1/2=cosϴ (1/2 + 1/2)=cosϴ (1+1/2)=cosϴ (2/2)=cosϴ (1)=cosϴ =R.H.S.Hence, it is proved that:See More
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