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Trigonometrical Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometrical Identities2 Marks
Question
Prove. $(cosA + sinA)^2 + (cosA - sinA)^2 = 2$
✓

Answer

$ \text{LHS} =(cosA + sinA)^2 + (cosA - sinA)^2$
$= \cos^2A + \sin^2A + 2cos A.\sin A + \cos^2A + \sin^2A - 2cos A.\sin A$
$= 2(\cos^2A + \sin^2A) = 2 = RHS$

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