Mathematics Trigonometric Identities MCQS Online Preparation Sample Paper Questions with Answer
ECAT Engineering Entry Test includes Mathematics Trigonometric Identities and tests the students on their knowledge of trigonometric identities and their usage. The various types of multiple-choice questions (MCQs) based on trigonometric identities commonly asked in various engineering entrance examinations include basic trigonometric identities, sum and difference identities, Pythagorean identities and co-function identities.
Nokryan to ensure students can shine. Be it Sample Papers, Practice Questions, or Solutions, everything is here on Nokryan.com. These materials are designed in a way that the students can learn the Mathematics Trigonometric Identities concepts with full confidence and can solve trigonometry-related questions in ECAT Mathematics promptly.
Understanding Trigonometric Identities
Trigonometric identities are fundamental equations that hold for all values of variables where the functions are defined. The key identities include:
Basic Trigonometric Identities:
- Reciprocal identities
- Quotient identities
- Even and odd function properties
Pythagorean Identities:
- sin2𝛼 + cos2𝛼 = 1
- 1 + tan2𝛼 = sec2𝛼
- 1+cot2α = csc2α
Sum and Difference Identities:
- sin( 𝛼 ± 𝛽) = sin𝛼 cos𝛽 ± cos𝛼 sin𝛽
- cos(α±β)=cosαcosβ∓sinαsinβ
Co-Function Identities:
- sin(𝛼 ± 𝛽) = sin 𝛼 cos𝛽 ± cos𝛼 sin𝛽
- cos(90∘ −α)=sinα
- tan(90∘ − 𝛼) = cot𝛼
Key MCQs on Mathematics Trigonometric Identities
1. tan(α – 90°)=
- -cot α correct
- – tan α
- cot α
- tan α
2. cos(π/2 – α)=
- cos α
- -cos α
- sin α correct
- -sin α
3. sin(π/2 – α)=
- -sin α
- csc α
- -cos α
- cos α correct
4. cot(90° – α) =
- -tan α
- -cot α
- -sin α
- tan α correct
5. sec (-α) =
- -sec α
- csc α
- sec α
- -cos α correct
6. tan (-α) =
- -tan α correct
- -cot α
- cot α
- tan α
7. sin (α – β) =
- sin α cos β – cos α sin βcorrect
- cos α cos β + sin α sin β
- sin α cos β + cos α sin β
- cos α cos β – sin α sin β
8. cot (-α) =
- -cot α correct
- cot α
- tan α
- -tan α
9. cos(α – 90°) =
- -csc α
- sin α correct
- -sec α
- csc α
10. sec(90° – α) =
- -sec α
- csc α correct
- -csc α
- sec α
11. sin(3π/2 – θ)=
- sin θ
- -sin θ
- cos θ
- -cos θ correct
12. sin (α + β) =
- cos α cos β + sin α sin β
- cos α cos β – sin α sin β
- sin α cos β + cos α sin β correct
- sin α cos β – cos α sin β
13. sin(90° – α) =
- -sin α
- cos α
- sin α
- -cos α correct
14. cot (α – 90°)=
- cot α
- -tan α correct
- tan α
- -cot α
15. csc(-α)=
- -csc α correct
- -cos α
- -sec α
- csc α
16. sin (-α)=
- Sec α
- -cos α
- sin α
- -sin α correct
17. cos(- α) =
- -sin α
- sin α
- cos α correct
- -cos α
18. cos (90° – α)=
- -sin α
- cos α
- -cos α
- sin α correct
19. cos (α + β) =
- sin α cos β + cos α sin β
- cos α cos β + sin α sin β
- sin α cos β – cos α sin β
- cos α cos β – sin α sin β correct
20. cos (α – β) =
- cos α cos β – sin α sin β
- cos α cos β + sin α sin β correct
- sin α cos β – cos α sin β
- sin α cos β + cos α sin β
21. csc (90° – α) =
- csc α
- sec α correct
- -sec α
- -csc α
22. csc (α – 90°) =
- csc α
- -sec α correct
- -cot α
- cot α
23. tan (90° – α) =
- -tan α
- -cot α
- cot α correct
- tan α
24. sin(α – 90°)=
- sin α
- csc α
- -sec α
- -cos α correct
25. sec(α – 90°)=
- csc α correct
- cot α
- -sec α
- -cot α
Why Mathematics Trigonometric Identities is Important for ECAT?
The Trigonometric Identities section is crucial in ECAT Mathematics, as it strengthens problem-solving skills required for engineering and physics applications. A strong grasp of these identities helps students simplify complex expressions and solve trigonometric equations effectively.
Prepare with Nokryan.com
Nokryan.com offers:
- ECAT sample papers and past MCQs
- Step-by-step solutions to trigonometry problems
- Topic-wise quizzes for better conceptual clarity
Regular practice ensures higher accuracy and speed in solving ECAT Mathematics MCQs, increasing the chances of securing admission into top engineering institutions.
Conclusion
The Mathematics Trigonometric Identities is a critical part of ECAT Mathematics content focusing on students covering fundamental, Pythagorean, sum-difference, and co-function identities. Through sufficient practice and a solid understanding of concepts, ECAT Engineering Entry Test students can comfortably work on trigonometry impressments. You will have also access to free resources on Nokryan.com. And you can do it with the help to maximize your prep and overall performance on the exam.