NEET/JEE Coaching Scholarship
Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes
Trigonometric identities provide a foundation that enables quick solutions to multiple mathematical expressions. This exercise demonstrates applying basic trigonometric ratios of sine, cosine and tangent when performing standard identity simplifications and verifications. The linkage among different trigonometric functions becomes possible through these identities, which enable us to show complex expressions in separate steps. Learning trigonometric connections helps students develop their logical reasoning skills, leading to advanced trigonometric abilities needed for engineering, architecture and physical science fields.
Exercise 8.3 in the NCERT Solutions for Class 10 presents three important identities which state
Q 1: Express the trigonometric ratios
Answer:
We know that
(i)
(ii) We know the identity of
(iii)
Q 3: Choose the correct option. Justify your choice
(A) 1 (B) 9 (C) 8 (D) 0
Answer:
The correct option is (B) = 9
And it is known that
Therefore, equation (i) becomes,
Q 3: Choose the correct option. Justify your choice
(A) 0 (B) 1 (C) 2 (D) –1
Answer:
The correct option is (C)
we can write his above equation as;
Q 3: Choose the correct option. Justify your choice
Answer:
The correct option is (D)
The above equation can be written as;
We know that
therefore,
Answer:
We need to prove-
Now, taking LHS,
LHS = RHS
Hence proved.
Answer:
We need to prove-
Taking LHS;
= RHS
Hence proved.
[ Hint: Write the expression in terms of
Answer:
We need to prove-
Taking LHS;
By using the identity a 3 - b 3 =(a - b) (a 2 + b 2 +ab)
= RHS
Hence proved.
[ Hint : Simplify LHS and RHS separately]
Answer:
We need to prove-
Taking LHS;
Taking RHS;
We know that identity
LHS = RHS
Hence proved.
Answer:
We need to prove -
Dividing the numerator and denominator by
Hence Proved.
Answer:
We need to prove -
Taking LHS;
By rationalising the denominator, we get;
Hence proved.
Q 4: Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
Answer:
We need to prove -
Taking LHS;
[we know the identity
Hence proved.
Answer:
Given the equation,
Taking LHS;
[since
Hence proved
[ Hint : Simplify LHS and RHS separately]
Answer:
We need to prove-
Taking LHS;
Taking RHS;
LHS = RHS
Hence proved.
Answer:
We need to prove,
Taking LHS;
Taking RHS;
LHS = RHS
Hence proved.
Also read-
1. Understanding basic trigonometric identities: You must learn the essential three trigonometric identities and understand their value for problem simplification and solution.
2. Verifying trigonometric identities: Perform proofs which establish two sides of an equation to be equal by using proper transformations in combination with trigonometric relations.
3. Developing logical and proof-solving skills: Step-by-step logical verification belongs to the set of skills that students need to develop for checking identities and producing mathematical proofs.
4. Preparing for advanced applications: Construct a strong foundation to solve problems utilising height-distance relationships alongside trigonometric equation methods, as well as actual angle measurement scenarios.
Check Out-
Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Yes, Exercise 8.3 is very important as identity-based questions frequently appear in CBSE Class 10 board exams
You should at least remember the fundamental identities and standard angle values to solve Exercise 8.3 effectively.
No, calculators are not allowed in Class 10 board exams, so you must rely on your memorised values and identities.
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
Register for ALLEN Scholarship Test & get up to 90% Scholarship
Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes
This ebook serves as a valuable study guide for NEET 2025 exam.
This e-book offers NEET PYQ and serves as an indispensable NEET study material.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters