Which of the following statement is correct?
1)cos 30°= tan 60°
2)cos 30° > tan 60°
3)cos 30° < tan 60°
4)None of these
Answers
Answer:
Option 3
cos 30° < tan 60°
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Answer:
In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:
(a)12/7
(b)24/7
(c)20/7
(d)7/24
Answer: (b)
Explanation: AB=24cm and BC = 7cm
Tan C = Opposite side/Adjacent side
Tan C=24/7
2. (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:
(a)0
(b)1+2√3
(c)1-√3
(d)1+√3
Answer: c
Explanation: sin 30° = ½, sin 60° = √3/2, cos 30° = √3/2 and cos 60° = ½
Putting these values, we get:
(½+½)-(√3/2+√3/2)
= 1-√3
3. The value of tan 60°/cot 30° is equal to:
(a)0
(b)1
(c)2
(d)3
Answer: b
Explanation: tan 60° = √3 and cot 30° = √3
Hence, tan 60°/cot 30° = √3/√3 = 1
4. 1-cos2A is equal to:
(a)sin2A
(b)tan2A
(c)1-sin2A
(d)sec2A
Answer: a
Explanation: We know, by trigonometry identities,
sin2A+cos2A = 1
1-cos2A = sin2A
5. Sin (90° – A) and cos A are:
(a)Different
(b)Same
(c)Not related
(d)None of the above
Answer: b
Explanation: By trigonometry identities.
Sin (90°-A) = cos A [comes in the first quadrant of unit circle]
6. If cos X = ⅔ then tan X is equal to:
(a)5/2
(b)√(5/2)
(c)√5/2
(d)2/√5
Answer: (c)
Explanation: By trigonometry identities, we know:
1+tan2X=sec2X
And sec X = 1/cos X = 1/(⅔) = 3/2
Hence,
1+tan2X=(3/2)2=9/4
tan2X=9/4-1=5/4
Tan X = √5/2
7. If cos X=a/b, then sin X is equal to:
(a)b2-a2/b
(b)b-a/b
(c)√(b2-a2)/b
(d)√(b-a)/b
Answer: (c)
Explanation: cos X=a/b
By trigonometry identities, we know that:
sin2X+cos2X=1
sin2X=1-cos2X = 1-(a/b)2
Sin X=√(b2-a2)/b
8. The value of sin 60° cos 30° + sin 30° cos 60° is:
(a)0
(b)1
(c)2
(d)4
Answer: b
Explanation: sin 60° = √3/2, sin 30° = ½, cos 60° = ½ and cos 30° = √3/2
Therefore,
√3/2 x √3/2 + ½ x ½
= 3/4 + 1/4
= 1
9. 2tan 30°/1+tan230° =
(a)Sin 60°
(b)Cos 60°
(c)Tan 60°
(d)Sin 30°
Answer: a
Explanation: tan 30° = 1/√3
Putting this value we get;
2(1/√3)/1+(1/√3)2 = (2/√3)/4/3 = 6/4√3 = √3/2 = sin 60°
10. sin 2A = 2 sin A is true when A =
(a)30°
(b)45°