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Question

In a triangle ABC the value of A is given by 5cosA+3=0, then the equation whose roots are sin A and tan A will be


A

15x2+8x16=0

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B

15x28x16=0

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C

15x28x+16=0

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D

15x282x+16=0

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Solution

The correct option is A

15x2+8x16=0


Given that 5cosA+3=0 or cosA=35

Let α=sin A and β=tanA, then the sum of roots

=α+β=sin A+tan A=sin A+sin Acos A=sin Acos A(1+cos A)

=192535(135)=45.53.25=815

and product of roots α.β= sin A tan A =sin2Acos A

=1625315=1625×53=1615

Thus required equation is x2(α+β)x+αβ=0

x2+8x151615=015x2+8x16=0


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