Question

if sinA+2cosA=1 then find 2sinA-cosA​

Answer 1

Step-by-step explanation:

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Answer 2

Given, sin A + 2 cos A = 1

Squaring both sides, we get,

sin2A + 4 cos2A + 4sinA cosA = 1

4 cos2A + 4sinA cosA = 1 - sin2A = cos2A

3 cos2A + 4sinA cosA = 0 ... (i)

Now, (2sinA - cosA)2 = 4sin2A + cos2A - 4sinA cosA

= 4sin2A + cos2A + 3cos2A [Using (i)]

= 4 (sin2A + cos2A) = 4

Thus, 2sinA - cosA = 2

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