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hovudverkocym6

hovudverkocym6

Answered question

2022-05-15

If
a b | sin x | d x = 8 and 0 a + b | cos x | d x = 9
then find the value of
( tan a . tan b )
For this type of question I am not able to open the values in modulus sign. I am not able to approach it

Answer & Explanation

exorteygrdh

exorteygrdh

Beginner2022-05-16Added 16 answers

Note that a b | sin x | d x = 0 b a | sin x | d x , because of periodicity and symmetry of | sin ( ) |.
Since
k π ( k + 1 ) π | sin x | d x = ( 1 ) k ( cos ( [ k + 1 ] π ) cos ( k π ) ) = 2
and
0 n π | sin x | d x = k = 0 n 1 k π ( k + 1 ) π | sin x | d x = 2 n ,
we have b a = 4 π
A similar argument for b a = 4 π yields a + b = 4.5 π.
The rest is solving this linear system of equations.

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