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Math Olympiad Test: Trigonometry- 2 - Class 10 MCQ


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15 Questions MCQ Test Olympiad Preparation for Class 10 - Math Olympiad Test: Trigonometry- 2

Math Olympiad Test: Trigonometry- 2 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The Math Olympiad Test: Trigonometry- 2 questions and answers have been prepared according to the Class 10 exam syllabus.The Math Olympiad Test: Trigonometry- 2 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math Olympiad Test: Trigonometry- 2 below.
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Math Olympiad Test: Trigonometry- 2 - Question 1

Which of the following is not possible?

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 1

Math Olympiad Test: Trigonometry- 2 - Question 2

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 2

We have 


∴ Both 1 and 2 are correct.

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Math Olympiad Test: Trigonometry- 2 - Question 3

Which among the following is true?

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 3

We know that, 1 radian = 180°/π = 57°30’ approx
57° lies between 0 and 90 degrees and since in first quadrant sin θ increases when θ increases
⇒ sin 1°< sin 1.

Math Olympiad Test: Trigonometry- 2 - Question 4

If sin θ − cosθ = 3/5, then sin θ cos θ =

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 4

Here sin θ − cosθ = 3/5
Squaring both sides, we get
sin2θ + cos2θ - 2 sin θ cos θ = 9/25
⇒ 1 - 2 sin θ cos θ = 9/25
⇒ 2 sin θ cos θ = 1 - 9/25 = 16/25
⇒ sin θ cos θ = 8/25

Math Olympiad Test: Trigonometry- 2 - Question 5

 If sin sin α = 4/5 and cos β = 4/5, then which of the following is true?

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 5

Math Olympiad Test: Trigonometry- 2 - Question 6

sinθ cos(90° - θ) + cosθ sin(90° - θ) ______.

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 6

Here sin θ cos(90 - θ) + cos θ · sin (90 - θ)
= sin θ · sin θ + cos θ · cos θ
= sin2θ + cos2θ = 1

Math Olympiad Test: Trigonometry- 2 - Question 7

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 7

Math Olympiad Test: Trigonometry- 2 - Question 8

If α = sec θ - tan θ and b = sec θ + tan θ, then

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 8

Given α = sec θ - tan  θ (i)
and b = sec  θ + tan  θ (ii)
Multiplying (i) and (ii) we get
sec2θ - tan2θ = α - b
⇒ 1 = ab
⇒ α = 1/b

Math Olympiad Test: Trigonometry- 2 - Question 9

 The value of tan 15° tan 20° tan 70° tan 75° is

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 9

We have tan 15 tan 20 tan 70 tan 75
= tan 15 tan 20 tan (90 - 20) tan (90 - 15)
= tan 15 tan 20 - cot 20 cot 15

= 1

Math Olympiad Test: Trigonometry- 2 - Question 10

If sin4θ - cos4θ = K4 then sin2θ - cos2θ is

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 10

a4 − b4 = (a2 − b2)(a2 + b2)

Math Olympiad Test: Trigonometry- 2 - Question 11

For all values of θ, 1 + cosθ can be ______.

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 11

Recall the range of cosθ.

Math Olympiad Test: Trigonometry- 2 - Question 12

If x = α (cosec θ + cot θ) and y = b (cot θ - cosec θ), then

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 12

We have,
x = a(cosecθ + cotθ)  ……. (1)
y = b(cosecθ − cotθ)  …….. (2)
From equation (1) and (2), we get
xy = ab(cosecθ + cotθ)(cosec − cotθ)
xy = ab(cosec2θ − cot2θ)
xy = ab[∵cosec2x − cot2x = 1]
Hence, this is the answer.

Math Olympiad Test: Trigonometry- 2 - Question 13

 is equal to

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 13

We have

Math Olympiad Test: Trigonometry- 2 - Question 14

The value of log sin 0° + log sin 1° + log sin 2° + ……. + log sin 90° is

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 14

Here log sin 0 + log sin 1 + log sin 2 + . . . + log sin 90
= log (sin 0 × sin 1 × sin 2 . . . sin 90)
= log (0) = 0

Math Olympiad Test: Trigonometry- 2 - Question 15

sin220° + cos2160° - tan245° =

Detailed Solution for Math Olympiad Test: Trigonometry- 2 - Question 15

sin220 + cos2160 - tan245 = sin220 + cos2160 - tan245
= sin2(180 - 160) + cos2160 - tan245
= sin2160 + cos2160 - tan245
= 1 - 1 = 0

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