Trigonometry
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(1 + tan²A) cotA is equal to cosec²A
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Expression = (1 + tan²A) cotA cosec²A
= sec²A . cotA . sin²A (sinA . cosecA = 1)= 1 . cosA .sin²A cos²A sinA = sinA = tanA cosA Correct Option: B
Expression = (1 + tan²A) cotA cosec²A
= sec²A . cotA . sin²A (sinA . cosecA = 1)= 1 . cosA .sin²A cos²A sinA = sinA = tanA cosA
- What is the value of sec 330°?
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sec 330° = sec (360° – 30°) = sec 30° = 2/3
[∵ sec (360° – θ) = secθ]Correct Option: D
sec 330° = sec (360° – 30°) = sec 30° = 2/3
[∵ sec (360° – θ) = secθ]
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If 1 = x, then the value of x is (tanA + cotA)
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1 = x tanA + cotB ⇒ 1 = x sinA + cosA cosA sinA ⇒ 1 = x sin²A + cos²A sinAcosA ⇒ 1 = sinA.cosA 1 sinAcosA Correct Option: A
1 = x tanA + cotB ⇒ 1 = x sinA + cosA cosA sinA ⇒ 1 = x sin²A + cos²A sinAcosA ⇒ 1 = sinA.cosA 1 sinAcosA
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What is the value of sin 
11π 
? 6
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sin 11π 6 = sin 2π - π 6
[∵ sin (360° – θ)
= sin (2π – θ) = –sin θ]= - sin π = - 1 6 2 Correct Option: C
sin 11π 6 = sin 2π - π 6
[∵ sin (360° – θ)
= sin (2π – θ) = –sin θ]= - sin π = - 1 6 2
- If secA + tanA = a, then the value of cosA is
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secA + tanA = a ..... (i)
∵ sec²A – tan²A = 1
⇒ (secA + tanA) (secA – tanA) = 1
² secA – tanA = 1/a ... (ii)
On adding equations (i) and (ii),2 secA = a + 1 = a² + 1 a a ⇒ secA = a² + 1 2a ⇒ cosA = 2a a² + 1 Correct Option: B
secA + tanA = a ..... (i)
∵ sec²A – tan²A = 1
⇒ (secA + tanA) (secA – tanA) = 1
² secA – tanA = 1/a ... (ii)
On adding equations (i) and (ii),2 secA = a + 1 = a² + 1 a a ⇒ secA = a² + 1 2a ⇒ cosA = 2a a² + 1
