MATHSTRIGONOMETRIC RATIOS & IDENTITIESTRIGONOMETRY

QUESTIONS ON TRIGONOMETRY (PART-5)

QUESTIONS ON TRIGONOMETRY (PART-5)

QUERY 41

If sec θ + tan θ = p, then sin θ is?

A) 1(p²+1)
B) 1(p²-1)
C) (p²+1)(p²-1)
D) (p²-1)(p²+1)

MAHA GUPTA
sec θ + tan θ = p (given)                                                                                  —- (i)

sec² θ – tan² θ = 1
=> (sec θ + tan θ)(sec θ – tan θ) = 1
=> sec θ – tan θ) =1p  (by putting sec θ + tan θ = p)        —- (ii)

By adding (i) and (ii)
2sec θ =p + 1p
=> (p²+1)p
=> sec θ = (p²+1)2p

By Subtracting (ii) from (i)
2 tan θ = p – 1p
=> (p²-1)p
=> tan θ = (p²-1)2p

sin θ = tan θsec θ = (p²-1)2p × 2p(p²+1)
= (p²-1)(p²+1) (option ‘D’)

QUERY 42

The value of cos 1° cos 2° cos 3° … cos 177° cos 178° cos 179° is?

A) 1√2
B) 0
C) 12
D) 1

MAHA GUPTA
cos 1° cos 2° cos 3° … cos 177° cos 178° cos 179°
= cos 1° cos 2° cos 3° … cos 90° … cos 177° cos 178° cos 179°
= cos 1° cos 2° cos 3° …× 0 × … cos 177° cos 178° cos 179°
= 0 (option ‘B’)

QUERY 43

If sin θ and cos θ are the roots of the equation ax² – bx + c = 0, then which one of the following is correct?

A) a² + b² + 2ac = 0
B) a² – b² + 2ac = 0
C) a² + c² + 2ab = 0
D) a² – b² – 2ac = 0

MAHA GUPTA
Sum of the roots
= sin θ + cos θ = -ba

Squaring both sides
sin² θ + cos² θ + 2sinθ cosθ = (-ba)² = —- (i)   

Product of the roots
= (sin θ)*(cos θ = ca

Putting sin² θ + cos² θ = 1 and product of the roots in (i)
1 + 2(ca) =
=> a² – b² + 2ac = 0 (option ‘B’)

QUERY 44

Value of tan 1° tan 2° tan 3° … tan 89° is?

A) 0
B) 1
C) -1
D) 2

MAHA GUPTA
tan 1° tan 2° tan 3° … tan 89°
= (tan 1° tan 89°)(tan 2° tan 88°)(tan 3° tan 87°) … (tan 45°)
= (tan 1° cot 1°)(tan 2° cot 2°)(tan 3° cot 3°) .. (tan 45)
= 1 × 1 × 1 × … × 1 = 1 (option ‘B’)

QUERY 45

One of the four angles of a rhombus is 60°. If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is?

A) 8√3 cm
B) 8 cm
C) 4√3 cm
D) 8√3 cm

MAHA GUPTA
Diagonals of a rhombus intersect at right angles
Therefore, in ΔAOB, OA ⊥ OB

 

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Maha Gupta

Maha Gupta

Founder of www.examscomp.com and guiding aspirants on SSC exam affairs since 2010 when objective pattern of exams was introduced first in SSC. Also the author of the following books:

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