Introduction to Trigonometry Test

Result

Introduction to Trigonometry Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

The value of the expression cosec (75° + θ)-sec(15°- θ)-tan(55°+ θ)+ cot (35° – θ) is

A
-1

B
0

C
1

D
3/2

Solution

(75°+θ) and (15°–θ) are complements of each other. Similarly, (55°+ θ) and (35°– θ) are also complements.

So, cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot (35° – θ)

= cosec[90° – (15° – θ)] – sec(15° – θ) –tan(55° + θ) + cot[90° – (55° + θ)]

= sec(15° – θ) – sec(15° – θ) – tan(55° + θ) + tan(55° + θ)

= 0

Hence, right option is (b).
Question 2
1 / -0

If cos 9α = sinα and 9α < 90°, then the value of tan 5α is

A
1/√3

B
√3

C
1

D
0

Solution

cos 9α = sinα

⇒ cos 9α = cos(90° - α)

⇒ 9α = 90° – α

⇒ 10α = 90°

⇒ α = 9°

∴ tan 5α = tan 5 × 9° = tan 45° = 1

Hence, verifies the option (c).