Grade 12Trigonometry

If 2SinA=2-CosA, find Sin A

Saurav Sinha

14 Years agoGrade 12

5 Answers

Chetan Mandayam Nayakar

14 Years ago

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

Ashwin Muralidharan IIT Madras

14 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 Years ago

3/5 or 1

Ishan

8 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

8 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