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Test: Trigonometric Functions- Case Based Type Questions


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10 Questions MCQ Test Mathematics (Maths) Class 11 | Test: Trigonometric Functions- Case Based Type Questions

Test: Trigonometric Functions- Case Based Type Questions for Commerce 2023 is part of Mathematics (Maths) Class 11 preparation. The Test: Trigonometric Functions- Case Based Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Trigonometric Functions- Case Based Type Questions MCQs are made for Commerce 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Trigonometric Functions- Case Based Type Questions below.
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Test: Trigonometric Functions- Case Based Type Questions - Question 1

A quadrilateral ABCD is inscribed in a circle as shown in the figure.

Based on the above data, answer the following question.

Q. The value of y is .............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 1 y = x + 40° = -15° + 40° = 25°
Test: Trigonometric Functions- Case Based Type Questions - Question 2

A quadrilateral ABCD is inscribed in a circle as shown in the figure.

Based on the above data, answer the following question.

Q. cos A + cos B + cos C + cos D = ...........

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 2 cos A + cos B + cos C + cos D

= cos A + cos B + cos(180° – A) + cos(180° – B)

= cos A + cos B – cos A – cos B = 0

Test: Trigonometric Functions- Case Based Type Questions - Question 3

A quadrilateral ABCD is inscribed in a circle as shown in the figure.

Based on the above data, answer the following question.

Q. cos(A + B + C + D) = .............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 3 Since ABCD is a quadrilateral,

A + B + C + D = 360°

cos(A + B + C + D) = cos 360° = 1

Test: Trigonometric Functions- Case Based Type Questions - Question 4

A quadrilateral ABCD is inscribed in a circle as shown in the figure.

Based on the above data, answer the following question.

Q. sin (B + D) = ..............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 4 Since ABCD is a cyclic quadrilateral,

B + D = 180° (opposite angles are supplementary)

∴ sin(B + D) = sin 180° = 0

Test: Trigonometric Functions- Case Based Type Questions - Question 5

A quadrilateral ABCD is inscribed in a circle as shown in the figure.

Based on the above data, answer the following question.

Q. The value of x is ..............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 5 A + C = 180°

⇒ - 4x + 4y + 20 = 180°

- 4x + 4y = 160°

x - y = - 40° ...(i)

B + D = 180°

⇒ 3y - 5 - 7x + 5 = 180°

- 7x + 3y = 180° ...(ii)

Solving (i) and (ii), x = –15°

Test: Trigonometric Functions- Case Based Type Questions - Question 6

A compound angle is an angle which can be expressed as the sum or difference of two standard angles.

Based on the above data, answer the following question.

Q. The value of tan 75° is = .............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 6 tan 75° = tan(45° + 30°)

=

=

= 2 + √3 (after rationalising denominator)

Test: Trigonometric Functions- Case Based Type Questions - Question 7

A compound angle is an angle which can be expressed as the sum or difference of two standard angles.

Based on the above data, answer the following question.

Q. sin(A + B).sin(A - B) = .............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 7 sin(A + B).sin(A – B)

= (sin A. cos B + cos A. sin B)(sin A. cos B - cos A. sin B)

= (sin A. cos B)2 - (cos A. sin B)2

= sin2 A. cos2 B - cos2 A. sin2 B

= sin2 A (1 - sin2 B) - (1 - sin2 A) sin2 B

= sin2 A - sin2 A. sin2 B - sin2 B + sin2 A. sin2 B

= sin2 A - sin2 B

Test: Trigonometric Functions- Case Based Type Questions - Question 8

A compound angle is an angle which can be expressed as the sum or difference of two standard angles.

Based on the above data, answer the following question.

Q. The value of cos 75° is ..............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 8 cos 75° = cos(30° + 45°)

= cos 30°.cos 45° – sin 30°.sin 45°

=

=

Test: Trigonometric Functions- Case Based Type Questions - Question 9

A compound angle is an angle which can be expressed as the sum or difference of two standard angles.

Based on the above data, answer the following question.

Q. 1 + cos 2A = ............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 9 cos 2 A = cos (A + A)

= cos A. cos A – sin A. sin A

= cos2 A – sin2 A

= cos2 A – (1 – cos2 A)

= 2 cos2 A – 1

∴ 1 + cos 2 A = 2 cos2 A

Test: Trigonometric Functions- Case Based Type Questions - Question 10

A compound angle is an angle which can be expressed as the sum or difference of two standard angles.

Based on the above data, answer the following question.

Q. The value of sin 75° is ..............

Detailed Solution for Test: Trigonometric Functions- Case Based Type Questions - Question 10 sin 75° = sin(30° + 45°)

= sin 30°.cos 45° + cos 30°.sin 45°

=

=

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