Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION

If   $\dpi{120} \fn_jvn \large cosA+sinA=\sqrt{2}cosA,$ Show that   $\dpi{120} \fn_jvn \large cosA-sinA=\sqrt{2}sinA$

EXPLANATION
Explain TypeExplanation Content
Text

CosA +sinA = √2cosAsquaring both sides.⇒(cosA + sin A)² = (√2cosA)²⇒cos²A + sin²A + 2sinAcosA = 2cos²A⇒1 - sin²A + 1 - cos²A + 2sinAcosA = 2cos²A⇒2 - 2cos²A = cos²A + sin²A - 2sinAcosA⇒2(1 - cos²A)= (cosA - sinA)²⇒ cosA - sinA = √[2sin²A]⇒cosA-sinA = √2sinAhence proved

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