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If 2SinA=2-CosA, find Sin A

If 2SinA=2-CosA, find Sin A

Grade:12

5 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

2sinA=2-cosA,cosA=2(1-sinA),1-sin2A=4(1-sinA)2

Ashwin Muralidharan IIT Madras
290 Points
11 years ago

Hi Saurav,

 

Let SinA = x.

So cosA = (1-x2)1/2.

Hence the eqn, 2x = 2 - (1-x2)1/2.

Or (1-x2)1/2 = 2 - 2x

Squaring, we have, 4+4x2-8x = 1-x2.

or 5x2 - 8x + 3 = 0.

(5x-3)(x-1) = 0.

 

So x = 1 or x = 3/5

So SinA = 1 or 3/5.

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

Rishabh Raj
14 Points
11 years ago

3/5 or 1

Ishan
21 Points
5 years ago
On squaring both sides,(2sinA)²=(2-cosA)²=> 4sin²A=4+cos²A-4cosA=>4sin²A=4+(1-sin²A)-4(2-2sinA)=>5sin²A=5-8+8sinA=>5sin²A-8sinA+3=0=>5sin²A-5sinA-3sinA+3=0=>5sinA(sinA-1)-3(sinA-1)=0=> (sinA-1)(5sinA-3)=0=> sinA=1, 3/5
Harsh Thakur
19 Points
5 years ago
2sinA=2-cosAcosA=2-2sinAcosA=2(1-sinA)Squaring both the sides(cosA) ^2=[2(1-sinA)]^2cos^2A=4(1-sinA)^21-sinA^2=4+4sin^2A-8sinA5sin^2A+3-8sinA=0Let sinA=x5x^2-8x+3=0Solve the quadratic equation further and replace x by sinATherefore you will get value of sinA= 1 or 3÷5

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