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 = a²                               —- (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 SSCEXAMFORUM.COM and guiding aspirants on SSC exam affairs since 2010 when objective pattern of exams was introduced first in SSC.

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