Direction: Study the following questions carefully and choose the right answer:
Important for :
1
What is cosec (75° + Θ) – sec (15° – Θ) – tan (55° + Θ) + cot (35° – Θ) equal to?
» Explain it
B
cosec (75° + Θ) – sec (15° – Θ) – tan (55° + Θ) + cot (35° – Θ)

= cosec (75° + Θ) – sec [90° – (75° – Θ)] – tan (55° + Θ) + tan [90 – (55° – Θ)]

= cosec (75° + Θ) – cosec (75° + Θ) – tan (55° + Θ) + tan (55° + Θ) = 0.

Hence, option B is correct.

2
If sin Θ.cos Θ = 1/2, then what is sin6Θ + cos6Θ equal to?
» Explain it
D
sin6Θ + cos6Θ = (sin2Θ)3 + (cos2Θ)3

= (sin2Θ + cos2Θ)(sin4Θ + cos4Θ – sin2Θcos2Θ)

= 1 [(sin2Θ + cos2Θ)2 – 3sin2Θcos2Θ]

 = 1 – 3 × 1 = 1 . 4 4

Hence, option D is correct.

3
 If 2 cot Θ = 3, so 2 cos Θ – sin Θ = 2 cos Θ + sin Θ

» Explain it
C
 2 cot Θ = 3  ⇒  cot Θ = 3 2

 = 2 cos Θ – sin Θ 2 cosΘ + sin Θ

[ Dividing by sin Θ in numerator & denominator]

=
 2. cos Θ – 1 sin Θ
=
 2 × 3 – 1 2
 2. cos Θ + 1 sin Θ
 2 × 3 + 1 2

 [ ∵ cos Θ = cot Θ = 3 ] sin Θ 2

 = 2 = 1 4 2

Hence, option C is correct.

4
In circular measure, the value of the angle 11° 15' is
» Explain it
A
11° 15'

 =  11° + 15° 60

 =  11° + 1 = 45° 4 4

[∵  180° = πc]

 ∴ 45° = π × 45 = πc 4 180 4 16

Hence, option A is correct.

5
 If 29 tanΘ=31, then 1+2sinΘ cosΘ = 1–2 sinΘ cosΘ

» Explain it
B
 29 tan Θ = 31  ⇒  tan Θ = 31 29

 Expression = 1 + 2sinΘ.cosΘ 1 – 2sinΘ.cosΘ

 = sin2 Θ + cos2Θ + 2sinΘ.cosΘ sin2Θ + cos2Θ – 2sinΘ.cosΘ

 = (sinΘ + cosΘ)2 (sinΘ – cosΘ)2

=
 sinΘ + cosΘ cosΘ cosΘ
2
 = tanΘ + 1 2 tanΘ – 1

 sinΘ – cosΘ cosΘ cosΘ

=
 31 + 1 29
2   =
 31 + 29 29
2
 31 – 1 29

 31 – 29 29

 = 60 2 = (30)2 = 900. 2

Hence, option B is correction.