# Trigonometry Part 7: Advance maths important questions.

Trigonometry Part 7: Advance maths important questions.

Q241. Meaning of equation sec2θ =holds for which of the following?

(a) x < y

(b) (x + y)2 > 4 xy

(c) (x + x) > 4 xy

(d) x = y

Q242. If sin2θ=1/4 and 0<θ<π then how many value of  θ will?

(a) 1

(b) 2

(c) 3

(d) 4

Q243. The value of sin 75°+cos 75° is

(a)

(b)

(c)

(d)

Q244. The value of sin2 5°+sin210°+sin285°+sin280°

(a) 1

(b) 2

(c) 3

(d) 4

Q245. Find the value of

(a) 1

(b) 0

(c) 3

(d) 6

Q246. If a = cos– cos  then which of the following statement is true?

(a) 0≤ a ≤ 1

(b) – 1 ≤ a ≤1

(c) – 1/4 ≤ a ≤ 0

(d) 0 ≤ a ≤ 1/2

Q247. is equall to

(a)9/16

(b) 7/16

(c) 5/16

(d) 3/16

Q248. If sec A + tan A = 4 then the value of sin A is

(a)8/15

(b) 15/17

(c)8/15

(d)8/17

Q249. (1 + cot A – cosec A) (1 + tan A+ sec A) is equal to

(a) 0

(b) 1

(c) 2

(d) 3

Q250.  is equal to

(a) 2 cosecθ

(b) 2 secθ

(c) 2 tanθ

(d) 2 cosθ

Q251.  value is equal to

(a) cot θ (1 – tan2θ)

(b) cot θ (sin2θ-1)

(c) cot θ . tan2θ

(d) tan θ . cosec2θ

Q252. Sin6 θ+ sin4θ cosθ -sin 2 θ. cos4 θ- cosθ=?

(a) sinθ – cos3 θ

(b) sin3 θ+ cos3 θ

(c) sin4 θ +cos4 θ

(d) sin2 θ– cos2 θ

Q253. The value of  is

(a)

(b)

(c)

(d)

Q254.  if α + β = π/2 and sin α = 1/3 then the value of sin β is

(a)√2/3

(b) 2√2/3

(c) 2/3

(d) 3/4

Q255. sin 50° -sin70° +sin10° = ?

(a) 1

(b) 2

(c) – 1

(d) 0

Q256. Value of tan 75° is

(a) 1 + 1/√3

(b) 2 – √3

(c) 2 + √3

(d) 1 +√3

Q257. Cos (A + B). cos (A – B) is equal to

(a) sin2A – sin2B

(b) cos2A – sin2B

(c) cos2 A – cos2B

(d) cos 2 A . sin 2B

Q258. If A + B + C = 180° than tan A + tan B + tan c is equal to

(a) 2 tan a tan B tan C

(b) tan A tan B tan C

(c) cot A cot B cot C

(d) tan A tan B tan C

Q259. If x = sec θ + tan θ  and y = sec θ – tan θ then relation between x and y is

(a) x2 + y2= 0

(b) x2 = y2

(c) x2 = y

(d) xy = 1

Q260. If  √3 cos θ + sin θ =1 then the value of θ is

(a) 0

(b) π/3

(c) π/6

(d) π/2

Q261. if tan θ =4/3 then value of is

(a) 1

(b) 2

(c) 3

(d) 4

Q262. The maximum value of cos θ -sin θ is

(a) √2

(b) 1

(c) 1/2

(d) 1/√2

Q263. The value of sin 105° . sin 75° is

(a)√3+2/4

(b) √3+2/2

(c) √3-2/4

(d)√3 2/2

Q264. if tanθ = √2 then θ is

(a) less than π/4

(b) equal to π/4

(c) between π/4 and π/6

(d) more than π/3

Q265. The value of tan 5° tan 10° tan 45° tan 80° tan 85° is

(a) 0

(b) 1

(c) – 1

(d) 1/2

Q266. tan 50° . tan 40° is equal to

(a) 0

(b) 1

(c) 2

(d) None of these

Q267. if 0≤ θ ≤ π and tan θ = cot θ is equal to

(a) 2π/3

(b) 3π /4

(c) 5π/6

(d) 4π/3

Q268. if 2 cosec θ = y= 1/y then cotθ is equal to

(a)

(b)

(c)

(d)

Q269. If then value of A is

(a) 45°

(b) 30°

(c) 15°

(d) 60°

Q270. The value of sin3a (1 + cot a) + cos3 a (1 + tan a)is

(a) sin a – cos a

(b) sin a + cos a

(c) sin a . cos a

(d) 1/sin a. cos a

Q271. If tanθ = 5/12 and 0° ≤ θ≤ 90° then is equal to

(a) 231/377

(b) 213/337

(c) 231/337

(d) -213/338

Q272. The value of sin6 a+ cos6a+ 3 sin2a cos2a is

(a) 0

(b) 1

(c) 1/2

(d) 1/4

Q273. . If tan θ + cot θ=2 then which of the following is the value of θ ?

(a) 60°

(b) 45°

(c) 30°

(d) 90°

Q274. If cos2 a + sin2a = tan2β then the value of cos2βsin2β is

(a) cot2β

(b) sin2a

(c) tan2a

(d) cos2a

Q275. If tan θ – coat θ =α and cosθ + sinθ = b then the value of (a2 + 4) (b2– 1)2 is

(a) 1

(b) 2

(c) 3

(d) 4

Q276. If x2 + y2 = 1, then the maximum value of xy

(a) 1/2

(b) -1/2

(c) 2

(d) – 2

Q277. The maximum value of sinθ + cosθ  is

(a) 1/4

(b) 1/2

(c) 1

(d) None of these

Q278. If α + β= 90° and a=2β` then cos2a +sin2β is

(a) 1

(b) ½

(c) 0

(d) 2

Q279. (tan θ + sec θ)2 is equal to

(a)

(b)

(c)

(d)

Q280. If θ =30° then the value of is

(a) 8

(b) 0

(c) 4

(d) 2

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