Q9:

Find the values of each of the following: $\tan \frac{1}{2}[\sin^{-1} \frac{2x}{1+x^2} + \cos^{-1} \frac{1-y^2}{1+y^2}]$, $|x| < 1$, $y > 0$ and $xy < 1$

I am a qualified and dedicated teacher, having 10 years of teaching and research experience across different boards including CBSE, ICSE, IGCSE, IB, GCSE, and Australian Board. I specialize in guiding students from Class 8 to Post Graduation, helping them achieve academic excellence with a tailored and engaging teaching approach. I bring in-depth knowledge and expertise to my sessions. Qualifications: • Ph. D (Science) – BIT Mesra, Ranchi • CSIR UGC NET (2011) AIR-14 • ICAR NET (2010) • ICAR NET (2018) • GATE (2009) My student-centered approach focuses on assessing individual learning needs, bridging knowledge gaps, and fostering critical thinking through interactive methods like discussions, visual aids, and hands-on activities. Regular feedback and personalized guidance empower students to excel and develop a lifelong love for learning.

I am an experienced, enthusiastic and well focused Teacher and I am giving home tuition since 2018. I am certified in B1. I also have a degree in B1. My key skills are Hardworking, Determined and Passionate. My accomplishments are Topper in A1 level, Class topper of Class 12 th and 1 st rank in College. I like to read novels in my free time and I want to promote education and well-being of children at all times. Always engaged in continuous learning in order to broaden my Knowledge and Experience.

I have over 10 years of experience teaching CBSE Class 12 Biology and Chemistry, helping students build a strong conceptual foundation while achieving excellent board examination results. My teaching methodology focuses on simplifying complex topics through clear explanations, logical reasoning, and regular practice. Every chapter is taught systematically from the NCERT textbook, ensuring students understand every concept thoroughly before progressing to application-based and board-level questions. My classes include detailed concept explanations, NCERT line-by-line learning, important diagrams, numerical problem-solving (Chemistry), previous years' board questions, competency-based questions, and chapter-wise assessments. I provide personalized attention by identifying each student's learning needs and adapting my teaching pace accordingly. Regular doubt-solving sessions, revision classes, mock tests, and performance analysis help students improve accuracy, confidence, and time management before the board examinations. My objective is not only to help students score high marks in the CBSE Class 12 Board Examination but also to develop a deep understanding of Biology and Chemistry, enabling them to confidently prepare for competitive examinations such as NEET. My classes are interactive, well-structured, and focused on helping every student achieve their academic goals through consistent guidance and disciplined practice.

I have around two years of experience in teaching. By profession, I am a spoken English trainer. Since 2016, I have been in this field. I hold a B.Sc degree from MGS University of Bikaner. I love to help students who want to be fluent in English. I'm well-versed in Hindi, English and Punjabi.

PHYSICS TUTORING WITH A PHYSICS EXPERT: STRATEGIES THAT MAKE SENSE FOR YOU! ABOUT SUBJECT Students will receive personalized instruction from a Physics expert. We will use the most successfully proven teaching techniques, and will also create brand new strategies to fit the students' individual needs. DESCRIPTION In this private tutoring session, I will thoroughly explain whatever Physics concepts you are currently struggling with, or we can learn new topics if you want to get ahead. I have taught Physics for over 5 years, and I am passionate about helping students understand it. Just name a topic of Physics (Mechanics, Heat, Wave, Electromagnetism, Modern Physics), and I will explain it in a way that makes the most sense to you. Then we will complete practice problems together to make sure you feel confident moving forward. I will also develop individualized strategies for you to use moving forward. Don't be surprised if I get really excited about the information you're learning - PHYSICS MAKES ME HAPPY AND I HOPE MY ENJOYMENT OF THE SUBJECT MAKES IT LESS INTIMIDATING TO YOU. Physics isn't your enemy; you just need someone to explain it in a way you understand. Please let me! Teacher Expertise I have a B.Tech degree in Computer Science and I have been teaching Physics exclusively for the past 5 years. ABOUT ME I am a Physics lover through and through! I've always said “PHYSICS DOESN'T HAVE TO BE HARD; YOU JUST NEED SOMEONE TO EXPLAIN IT IN A WAY YOU UNDERSTAND." I can do that! I’m passionate about helping students gain confidence and mastery in Physics. Physics is my favorite subjects, so you'll see me get really excited about them! When I teach, I customize my strategies to fit your individual needs, and I have so many tricks up my sleeve for teaching Physics concepts, I can always find a method that works for you. And of course, it is especially important to me to make sure every student feels safe to make mistakes in my class – we celebrate mistakes! The only way to master Physics is to learn from your mistakes! I've taught JEE & NEET Physics online for 5 years and in coaching industry for over 5 years. It's a real pleasure to help students achieve their goals in IIT-JEE & NEET.