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 Sum

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

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

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

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

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

(vi)  \cot A \cdot \cot B =\dfrac{\cot A+\cot B}{\tan A+\tan B}

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

(viii) \cot A \cdot \tan B=\dfrac{\cot A +\tan B}{\tan A +\cot B}

Powers of Trigonometric Functions:

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

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

(iii)  \sin^3A=\dfrac{3\sin A -\sin 3A}{4}

(iv) \cos^3A=\dfrac{3 \cos A +\cos 3A}{4}

(v) \sin ^4A=\dfrac{\cos 4A-4\cos 2A+3}{8}

(vi) \cos^4A=\dfrac{\cos4A+4\cos 2A+3}{8}

(vii)  \sin^5A=\dfrac{10 \sinA -5 \sin3A+\sin 5A}{16}

(viii)  \cos^5 A=\dfrac{10 \cos A +5 \cos 3A+\cos 5A}{16}

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