Gagan Pratap Advance Maths Complete Class Notes Exclusive ^hot^ Jun 2026

These are handwritten (or digitized from handwritten) notes that capture specific "class-only" tips and tricks not found in standard textbooks.

Explanation: $a^2 - 2a + 1 + b^2 - 2b + 1 + c^2 - 2c + 1 = 0$. $(a-1)^2 + (b-1)^2 + (c-1)^2 = 0$. This implies $a=1, b=1, c=1$. We need $a^3+b^3+c^3 - 3abc$. Since $a=b=c=1$, the term is a determinant of zero rows/columns logic, or simply $1+1+1 - 3(1) = 0$. gagan pratap advance maths complete class notes exclusive

Explanation: Square both: $\cos^2 + \sin^2 + 2\cos\sin = 2\cos^2$. $1 + 2\sin\cos = 2\cos^2 \implies 1 = 2\cos^2 - 2\sin\cos$. Also, given $\cos + \sin = \sqrt2\cos \implies \sin = (\sqrt2-1)\cos$. $\frac\sin\cos = \tan \theta = \sqrt2-1$. Question asks for $\frac\cos\sin = \cot \theta = \frac1\sqrt2-1 = \sqrt2+1$. These are handwritten (or digitized from handwritten) notes

In this article, we explore why these exclusive notes are a game-changer and how you can leverage them to conquer the toughest section of the competitive exam syllabus. Why Advance Maths is the Ultimate Rank Decider This implies $a=1, b=1, c=1$

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