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The number of values of theta which satisfy the equation 6sin ^( 3 )theta+ 25sin ^( 2 )theta- 39sin theta- 70 = 0 is ]

The number of values of theta which satisfy the equation 6sin^(3)theta+25sin^(2)theta-39sin theta-70=0 is ]

Grade:11

1 Answers

Aditya Gupta
2075 Points
one year ago
Let sinx=s.
So 6s^3 is less than or equal to 6.
25s^2 is less than or equal to 25.
-39s is less than or equal to 39.
Add all these inequalities to get
6s^3+25s^2-39s is less than or equal to 70.
But this expression is given to be equal to 70 in the question. Hence equality should hold in all cases, i.e, 6s^3=6, 25s^2=25, -39s=39.
However, there exists no value of s for which all these equations simultaneously hold true. Hence, no/zero solutions exist.
KINDLY APPROVE :))

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