Assignment No. 2 of MTH 102
Question No.1:
If = 17, =37, find the first term, common difference and .
Solution:
Given Data:
=17
=37
Find out
First term=
Common difference= d
6^{th} term=
Formula:
So,
=
17=
And
= =37
37=
Subtracting equation (i) from equation (ii)
We get,
20= 4d
d= 20/4
d=5
So the common difference is 5.
Putting d=5 in equation .1
We get
17=
17=
So the first term is -3.
From above formula we can find 6^{th} term
So,
So the 6^{th} term is 22.
Question no. 2:
Find the value of sin 105 )
Solution:
=sin 105
=sin (60
According 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 B
So,
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= /2
Now 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:
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