Numerical
If tanA and tans are the roots of the quadratic equation, 322 - 10.- 25 = 0,
then the value of
3sin (A + B) – 10sin(A + B). cos(A+B) - 25cos(A+B) is
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If tanA and tanB are the roots of the quadratic equation, 3x
2
−10x−25=0, then the value of 3sin
2
(A+B)−10sin(A+B)cos(A+B)−25cos
2
(A+B) is:
December 20, 2019avatar
Anushka Ahsan
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ANSWER
Given, 3x
2
−10x−25=0
tanA+tanB=
3
10
tanA×tanB=
3
−25
tan(A+B)=
1−tanAtanB
tanA+tanB
1+
3
25
3
10
3
28
3
10
=
28
10
=
14
5
∴tan(A+B)=
14
5
∴sin(A+B)=
221
5
cos(A+B)=
221
14
∴3sin
2
(A+B)−10sin(A+B)cos(A+B)−25cos
2
(A+B)
=3×
221
25
−10×
221
70
−25×
221
196
=
221
75−700−4900
=−25
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