# SSC Trigonometry Practice Paper (Part 12): Advance maths important questions

SSC Trigonometry Practice Paper : Advance maths important questions

Q441. If a cos θ + b sin θ  = p and a sin θ – b cos θ q , then the relation between a, b, p and q is

(a) a 2 – b 2 = p 2 – q 2

(b) a 2 + b 2 = p 2 + q 2

(c) a + b = p + q

(d) a – b = p – q

Q442. If (sinα + cosecα)² +(cos α + sec α)²  = k + tan²α + cot²α , then the value of k is

(a)  1

(b)  7

(c)  3

(d)  5

Q443. If sin 21º x/y , then sec 21º – sin 69º is equal to

(a)

(b)

(c)

(d)

Q444. If sec α + tan α = 2 ,then the value of sin α is (assume that 0, α < 90º)

(a)    0.4

(b)    0.5

(c)    0.6

(d)    0.8

Q445. If 3 sin θ + 5 cos θ = 5, then the value of 5 sin  θ – 3 cos θ will be

(a)   ± 3

(b)   ± 5

(c)   ± 2

(d)   ± 1

Q446. If  is an acute angle and tan θ + cot θ = 2, then the value of tan5θ+ cot5θ is

(a)    1

(b)    2

(c)    3

(d)   4

Q447. The simple value of tan 1º. tan 2º. Tan 3º…..tan 89º is

(a)   1/2

(b)    0

(c)    1

(d)   2/3

Q448. If x sin2 60º – 3/2 sec 60º tan2 30º +  4/5 sin2 45º tan60º = 0 then x is

(a)   –  1/15

(b)   -4

(c)  – 4/15

(d)  – 2

Q449. If 7 sin α  = 24 cos α ; 0 <α<Π/2 , then the value of 14 tan α – 75 cos α – 7 sec α is equal to

(a)    3

(b)   4

(c)    1

(d)    1

Q450. The value of x which satisfies the equation 2 cosec2 30º + x sin2 60º – 3/4 tan2 30º = 10 is

(a)    2

(b)    3

(c)    0

(d)    1

Q451. If 2 sinθ  + cosθ  = 7/3 then the value of (tan-sec) is

(a)     0

(b)    -1

(c)   3/7

(d)   7/3

Q452. If 29 tan = 31, then the value of  is equal to

(a)     810

(b)    900

(c)    540

(d)    490

Q453. ABCD is a rectangle of which AC is a diagonal.  The value of (tan2 ΔCAD+1) sin2ΔBAC is

(a)    2

(b)   1/4

(c)    1

(d)    0

Q454. If tan x = sin 45º. Cos 45º + sin 30º then the value of x is

(a)    30º

(b)    45º

(c)    60º

(d)    90º

Q455. For any real values of,

(a)   cotθ – cosecθ

(b)   secθ – cotθ

(c)   cosecθ – cotθ

(d)   tanθ  – secθ

Q456. If the sum and difference of two angles are 135º and Π respectively, then the value of the angles in degree measure are

(a)    70º, 65º

(b)    75º, 60º

(c)    45º, 90º

(d)    80º, 55º

Q457. In a  ΔABC, ΔB = Π and D divides BC internally in the ration 1 : 3 then  is equal to

(a)    1/√2

(b)   1/√3

(b)   1/√6

(d)   √6

Q458. If sin 3A = cos (A-26º), where 3A is an acute angle then the value of A is

(a)   29º

(b)   26º

(c)   23º

(d)   28º

Q459. Value of   sec²θ

(a)     1

(b)    2

(c)     2

(d)   -2

Q460. If sin + cos), y = b (sin – cos) then the value of  is

(a)   0

(b)    1

(c)    2

(d)   -2

Q461. If sin 5 θ = cos 20º (0º<θ< 90º) then the value of θ is

(a)    4º

(b)    22º

(c)    10º

(d)    14º

Q462. If 0º<θ< 90º and 2 sec θ  = 3 cosecθ, then  is

(a)  Π/6

(b)  Π/4

(c)   Π/3

(d)   Π/5

Q463.is equal to

(a)   2 cos

(b)   2 sin

(c)   2 cot

(d)   2 sec

Q464. If cos θ = 3/5 , then the value of sin θ. sec θ. tan θ is

(a)    9/16

(b)    16/9

(c)    3/4

(d)   4/3

Q465. If 0º< A < 90º, then the value of tan2A + cot2A – sec2A cosec2A is

(a)   0

(b)   1

(c)   2

(d)   -2

Q466. If α and β are positive acute angles, sin(4 α- β ) = 1 and cos(2 α+ β) =  1/2, then the value of sin(α+2β) is

(a)   0

(b)   1

(c)   √3/2

(d)   1/√2

Q467. The value of  equal to

(a) sinθ

(b) cosθ

(c) tanθ

(d) cotθ

Q468. If θ is a positive acute angle and 4 cos2 θ – 4 cos θ + 1 = 0, then the value of tan (θ – 15º) is equal to

(a)     0

(b)     1

(c)   √3

(d)  1/√3

Q469. If (r cos θ –  √3)2 + (r sin θ-1)2 = 0 then the value of   is equal to

(a)   4/5

(b)   5/4

(c)   √3/4

(d)   √5/4

Q470. The value of

(a)  – 1

(b)    0

(c)     1

(d)    2

Q471. If sin (θ+18º) = cos 60º(0<θ<90º), then the value of cos 5 θ is

(a)    1/2

(b)   0

(c)   1/√2

(d)   1

Q472. If tan θ = 3/4 , then the value of  is equal to

(a)   1/21

(b)  2/21

(c)  4/21

(d)  8/21

Q473. If then sin2  β  is equal to

(a)

(b)

(c)

(d)

Q474. Let A, B, C, D, be the angles of a quadrilateral.  If they are concylic, then the value of cos A + cos B + cos C + cos D is

(a) 0

(b) 1

(c) -1

(d) 2

Q475. If √3 tan θ= 3 sin θ , then the value of (sinθ – cosθ) is

(a) 1

(b) 3

(c)

(d) None

Q476. If sin (A+B) = sin A cos B + cos A sin B, then the value of sin 75º is

(a)

(b)

(c)

(d)

Q477. ABC is a right angled triangle, right angled at B and ΔA =  60 º and AB = 20 cm, then the ration of sides BC and CA is

(a)  √3: 1

(b) 1 :√3

(c)  √3:√2

(d)  √3: 2

Q478. If tan 2 θ. Tan 3 θ = 1, where 0 º< θ < 90 º then the value of θ is

(a) 22½º

(b) 18 º

(c) 24 º

(d) 30 º

Q479. If cos2α- sin2α= tan2β, then the value of cos2β – sin2β is

(a) cotα

(b) cot2 β

(c) tan2 α

(d) tan2 β

Q480. The tan (A+B) = √3  and tan (A-B) = 1/√3,ΔA+ΔB ) < 90 º, A ≥ B, then ΔA is

(a) 90 º

(b) 30 º

(c) 45 º

(d) 60 º

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