Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Transforming of Trigonometric Expression to Product

(i)  \sin A+\sin B=2 \sin \dfrac{A+B}{2}\cdot \cos \dfrac{A-B}{2}

(ii)  \sin A-\sin B=2 \cos \dfrac{A+B}{2} \cdot \sin \dfrac{A-B}{2}

(iii)  \cos A+\cos B=2 \cos \dfrac{A+B}{2}\cdot \cos \dfrac{A-B}{2}

 \begin{aligned} (iv)\cos A-\cos B& =-2 \sin \dfrac{A+B}{2} \cdot \sin \dfrac{A-B}{2} \\ \text { or }&= 2 \sin \dfrac{A+B}{2}\cdot \sin \dfrac{B-A}{2} \end{aligned}

(v)  \tan A+\tan B=\dfrac{\sin (A+B)}{\cos A \cdot \cos B}

(vi)  \tan A-\tan B=\dfrac{\sin (A-B)}{\cos A \cdot \cos B}

(vii)  \cot A +\cot B =\dfrac{\sin (B+A)}{\sin A \cdot \sin B}

(viii)  \cot A -\cot B =\dfrac{\sin (B-A)}{\sin A \cdot \sin B}

\begin{aligned} (ix) \cos A +\sin A &= \sqrt{2} \cos \left( \dfrac{\pi}{4}-A \right)\quad (i)\\&= \sqrt{2} \sin \left( \dfrac{\pi}{4}+A \right)\quad (ii) \end{aligned}

\begin{aligned} (x) \cos A -\sin A &= \sqrt{2} \sin \left( \dfrac{\pi}{4}-A \right)\quad (i)\\&=\sqrt{2}\cos \left( \dfrac{\pi}{4}+A \right) \quad (ii) \end{aligned}

(xi) \tan A+\cot B=\dfrac{\cos (A-B)}{\cos A \cdot \cos B}

(xii) \tan A-\cot B =-\dfrac{\cos (A+B)}{\cos A \cdot \cos B}

(xiii)  1+ \cos A =2 \cos^2 \dfrac{A}{2}

(xiv) 1- \cos A =2 \cos^2 \dfrac{A}{2}

(xv) 1+\sin A =2 \cos^2 \left( \dfrac{\pi}{4}-\dfrac{A}{2} \right)

(xvi)  1-\sin A =2 \sin ^2 \left( \dfrac{\pi}{4}-\dfrac{A}{2} \right)

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