Aptitude TrigonometryPage 3
17. | | If 1 + sin2 A = 3 sin A cos A, then what are the possible values of tan A? | | (a)1/4, 2 | | (b)1/6, 3 | | (c)1/2, 1 | | (d)1/8, 4 |
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Answer is: CIn the given equation,
1 + sin2/sup> A = 3 sin A cos A
Dividing both sides by cos 2
We get, 1/cos2 A + sin2 A/cos2 A = 3 x sin A/cos A
sec2 A + tan2 A = 3 tan A
1+ tan2 A + tan2 A = 3 tan A
2 tan2 A - 3 tan A +1 = 0
2 tan2 A – 2 tan A – tan A + 1= 0
2 tan A (tan A – 1) – 1(tan A – 1) = 0
(2 tan A – 1) (tan A – 1) = 0
tan A = 1/2, 1
18. | | If cos4 X - sin4 = 2/3 = , then the value of 2 cos2 X - 1 is | | (a)0 | | (b)1 | | (c) | | (d) |
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Answer is: Ccos4 X - sin4 = 2/3
(cos2 X + sin2)(cos2 X - sin2) = 2/3
cos2 X - sin2 = 2/3
cos2 X - (1 - cos2) = 2/3
2 cos2 X - 1 = 2/3
19. | If tan (X1 + X2) = √3 and sec (X1 - X2) = 2/√3, then the value
of sin 2X1 + tan 3X2 is equal to (assume that 0 < X1 - X2 < X1 + X2 < 90o) | | (a)2 | | (b)3 | | (c)4 | | (d)5 |
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Answer is: Atan (X1 + X2) = √3 = tan 60o
X1 + X2 = 60o and sec (X1 + X2) = 2/√3 = sec 30o
X1 - X2 = 30o
∴ X1 = 45o and X2 = 15o
∴ sin 2X1 + tan 3X2
= sin 90o + tan 45o
= 1 + 1 = 2
20. | | The minimum value of 2 sin2 X + 3 cos2 X is | | (a)0 | | (b)3 | | (c)2 | | (d)1 |
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Answer is: B2 sin2 X + 3 cos2 X
= 2 sin2 X + 2 cos2 X + cos2 X
= 2 (sin2 X + cos2 X) + cos2 X
= 2 + cos2 X
∴ Minimum value of cos X = -1
∴ Required minimum value = 2 + 1 = 3
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