Can you solve IIT-JEE 2026 Question?
A math educator solves an IIT-JEE 2026 trigonometry problem involving a quadratic equation whose roots are tan(a) and tan(b). Using Vieta's formulas and trigonometric identities, the presenter derives the value of 20·sin²((a+b)/2), arriving at the answer 10 - 3√10. The video is framed around the presenter's personal connection to IIT-JEE results from 9 years ago.
Summary
The video opens with the presenter acknowledging that IIT-JEE results were announced the previous day, and reflecting that their own JEE result 9 years ago changed their life completely. This personal anecdote sets a motivational tone before diving into the mathematical problem.
The problem presented is the quadratic equation x² - 2x - 5 = 0, where tan(a) and tan(b) are given as its roots. Using Vieta's formulas, the presenter identifies that tan(a) + tan(b) = 2 (i.e., -b/a = -(-2)/1) and tan(a)·tan(b) = -5 (i.e., c/a = -5/1).
With these values, the presenter applies the tangent addition formula: tan(a+b) = (tan a + tan b) / (1 - tan a·tan b) = 2 / (1 - (-5)) = 2/6 = 1/3.
A right triangle is then constructed with tan(a+b) = 1/3, giving opposite side = 1, adjacent side = 3, and hypotenuse = √10. This yields cos(a+b) = 3/√10.
Finally, the half-angle identity sin²(θ/2) = (1 - cosθ)/2 is applied with θ = a+b, giving sin²((a+b)/2) = (1 - 3/√10)/2 = (√10 - 3)/(2√10). Multiplying by 20 (as implied by the problem's expression 20·sin²((a+b)/2)) gives the final answer: 10 - 3√10, which corresponds to option D.
Key Insights
- The presenter uses Vieta's formulas to extract tan(a) + tan(b) = 2 and tan(a)·tan(b) = -5 directly from the quadratic x² - 2x - 5 = 0 without solving for individual roots.
- The presenter applies the tangent addition formula tan(a+b) = (tan a + tan b)/(1 - tan a·tan b), substituting the Vieta values to get tan(a+b) = 2/6 = 1/3.
- The presenter constructs a right triangle with tan(a+b) = 1/3 to geometrically determine that cos(a+b) = 3/√10, avoiding abstract algebraic manipulation.
- The half-angle identity sin²(θ/2) = (1 - cosθ)/2 is identified as a key formula that must be memorized to solve this problem, according to the presenter.
- After multiplying sin²((a+b)/2) by 20 as required by the problem, the presenter arrives at the final answer 10 - 3√10, identifying option D as correct.
Topics
Transcript
[0:00] नमस्ते एवरीवन। कल आईआईटी जेई का रिजल्ट आया है। आज से 9 साल पहले मेरा भी जेई का रिजल्ट आया था। जिसके बाद मेरी पूरी जिंदगी बदल गई। देखते हैं आप 2026 का सवाल सॉल्व कर पाते हैं या नहीं। इक्वेशन है x² - 2x - 5 = 0 और हमारा दिया गया है कि tan a और tan b जो है वो इसके रूट्स हैं। तो हम tan a + tan b क्या लिख सकते है? - b / a यानी कि टू और tan a * tan b हम क्या लिख सकते है? ये हम लिख सकते हैं -5 क्योंकि c / a होता है। और ये हमारा यहां से वन है। अब अगर हम यहां पे…
Full transcript available for MurmurCast members
Sign Up to AccessMore from IIT-IIM Unfiltered
Is Reservation Killing IIT-IIM Placements?
A speaker analyzes IIM Lucknow placement data by category, revealing that General category students achieve higher average placements but some perform poorly, while reserved category students often work harder due to awareness of their disadvantages. The speaker argues that MBA placements are biased toward candidates with strong backgrounds and soft skills, unlike technical fields that prioritize coding skills.
Why are INDIANS so INSECURE
The speaker argues that Indians suffer from an inferiority complex that causes them to seek external validation and focus excessively on perceived racism and discrimination. He advocates for building internal confidence as a population rather than constantly seeking validation from the world.
3 STRATEGIES to ACE MATH EASILY | Cleared IIT JEE, CAT, XAT, SSC CGL, RBI Grade B, UPSC CDS
A mathematics educator who scored 90%+ in competitive exams like IIT JEE, CAT, and SSC CGL shares three core strategies: visualization (understanding steps before solving), formula mastery (memorizing or deriving formulas rather than guessing), and fundamentals over tricks (thoroughly completing NCERT coursework multiple times). The speaker demonstrates these principles through an IIT JEE complex number problem.
Zindagi ka Goal - Shaadi
A 27-year-old Indian woman addresses constant social pressure about her unmarried status, explaining three key reasons she refuses to rush into marriage. She discusses financial preparedness for future children, finding the right compatible partner, and resisting societal pressure as her guiding principles.
How I scored 156 in SSC CGL Tier-1 ➤ 3 Honest Strategies and FREE Resources
A consultant who scored 156 in SSC CGL Tier-1 shares her three-pillar strategy for clearing the exam using only free resources and books, without any coaching classes. Her approach centers on taking mocks from Day 1, covering every subject, and maintaining confidence during the exam. She emphasizes analyzing mock tests to identify weak topics and allocating time strategically across subjects.