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notka56 [123]
3 years ago
13

Let cos x =1√10 with x in QIV and find: cot2x

Mathematics
1 answer:
Mazyrski [523]3 years ago
3 0
Cos x = 1/√10
sin x = √( 1 - 1 /10 ) = √9/10 = - 3/√10 ( because x is in Q IV )
cot 2 x = cos 2 x/sin 2x = ( cos²x - sin²x)/ (2 sinx cosx ) =
= ( 1/10 - 3/10 )/(2 * (-3/√10)*1/√10)= (- 8/10 ) / (-6/10 ) = 8/6 = 4/3
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Write a rule for the nth term of the arithmetic sequence:<br><br> a11= 50, d = 7
ivolga24 [154]

Answer:

Required rule for n^{th} is a_{n}=7n-27.

Step-by-step explanation:

Given that,

a_{11} = 50,\  \  d=7

From the question: we have to write the n^{th} term of Arithmetic sequence.

Arithmetic Sequence or Arithmetic progression (A.P) : It is a sequence which possess that difference between of two successive sequence is always constant.

                a_{1} ,a_{2},a_{3},a_{4}.....................a_{n-1},a_{n}

                                        where, a_{1} is the first term of A.P

                                                     d is the common difference.

                                                     a_{n} is the last term or general term.

The above sequence to be in A.P then their common difference should be equal.

          d=a_{2}-a_{1} =a_{3}-a_{2}=a_{4} -a_{3} ..........................a_{n}-a_{n-1}

Now, Formula of General Term is a_{n}=a+(n-1)d

So,                                                    a_{11}= a+(11-1)d\\        a_{11} = a+10d

 Substituting the value of   a_{11} = 50,\  \  d=7 we get,

                                                         50=a+10\times7\\50=a+70\\a=-20

Then General term (a_{n}) of given data is

                                                         a_{n}=-20+(n-1)7\\a_{n}=-20+7n-7\\a_{n}=7n-27

Therefore, Required rule for n^{th} is a_{n}=7n-27.

5 0
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