Question

$\huge \mathfrak \color{green}{question} :$
If cosA + SinA = √2 CosA , prove that CosA - SinA = √2SinA. ​

Answer 1

$\huge \sf \color{purple}{\underline{Solution}} :$

Considering CosA + SinA = √2 CosA ...(i)

Squaring we get ,(CosA + SinA)² = 2Cos²A

⟹ Cos²A + sin²A +sinAcosA = 2cos²A

⟹ 2sinA cosA = cos²A - sin²A

⟹ cos²A - sin²A = 2sinA cosA ....(ii)

$\colorbox{lightgreen}{\sf Dividing \: (ii) \: by \: (i) \: we \: get , }$

$\large \sf \implies \frac{cos²A - sin²A}{cosA - sinA} = \frac{2sinAcosA}{\sqrt{2}cosA}$

⟹ cosA - sinA = √2 sinA.

$\huge \underline{hence \: proved}$

Answer 2

Hey mate,

Hey mate,Here is your answer :- ⟹ cosA - sinA = √2 sinA.