Mth 102 Assignment no.2 solution fall 2021

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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:

[+ M.Tariq Malik]

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