If cos A + sin A = √2 sinA , Then, Find sin A - cos A

2 sinA

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√2 sinA

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2 cosA

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√2 cosA

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Solution

The correct option is D
√2 cosA

cos A = √2 sin A - sin A

cos A = (√2 - 1)sin A

sin A = cos A/(√2 – 1) and then rationalising the denominator we get
sin A - cos A = √2 cosA

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Similar questions

If Cos A + sin A= 2 cos A show that Cos A-sinA= 2 Sin A.

If sinA + 2cosA = 1. Prove that 2sinA -cosA= 2.

\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{2 s i n^{2} A - 1}

If sin A + 2cos A = 1

Prove That 2sin A - cos A = 2

Please explain with full steps

\sqrt{2}

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