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If sinA +2cosA=1 prove that 2sinA-cosA=2

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If sinA +2cosA=1 prove that 2sinA-cosA=2

Posted by Dilip Sidam 5 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 10 months ago

Given that Sin A + 2 cos A = 1

Squaring on both sides, we get

(sin A + 2 cos A)² = 1

We know that (a+b)² = a² + b² + 2ab.

(sin² A + 4 cos² A + 4 sin A cos A) = 1

4 cos² A + 4 sin A cos A = 1 - sin² A

4 cos² A + 4 sin A cos A = cos² A

3 cos² A + 4 sin A cos A = 0

3 cos² A = - 4 sin A cos A ---- (1).

Given 2 sin A - cos A

Squaring on both sides, we get

(2 sin A - cos A)² = 4 sin² A + cos² A - 4 sin A cos A

= 4 sin² A + cos² A + 3 cos² A

= 4 sin² A + 4 cos² A

= 4(sin² A + cos² A)

= 4.

2 sin A - cos A = 2.

1Thank You

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