Question

If 2 cos θ = 2-sin θ. Then what is the value of cos θ ?

Answer 1

$\bf{hey!!!}$

From given :-

2cos¢ = 2 - sin¢

2 - 2cos¢ = sin¢

squaring on both side ^^

we get ,

(2- 2cos¢ )² = (sin¢ )²

4 + 4cos²¢ - 8cos¢ = sin²¢

4 + 4cos²¢ - 8cos¢ - sin²¢ =0

4cos²¢ - sin²¢ - 8cos¢ + 4 =0

4cos²¢ - ( 1 - cos²¢ ) - 8cos¢ + 4 =0

4cos²¢ - 1 + cos²¢ - 8cos¢ + 4 =0

5cos²¢ - 8 cos¢ + 3 = 0

just using this term as quadratic equation .. just imagine cos¢ = x
then we get

5cos²¢ - 5co¢¢ - 3cos¢ + 3 = 0

5 cos¢ ( cos¢ - 1 ) - 3 ( cos¢ - 1 ) = 0

( 5cos¢ - 3) ( cos¢ - 1 ) = 0
<< [taking common terms]

( 5cos¢ - 3) = 0

cos¢ = 3/5

and similarly ..

cos¢ - 1 = 0

cos¢ = 1

Hence, cos¢ = 1 and 3/5 Answer ✔

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$\boxed{hope \: it \: helps \: you}$
$\underline{rajukumar111}$

Answer 2

Your answer is ---

we have ,

2 cosθ = 2 - sinθ

taking square both side, we get

4 cos^2θ = 4 + sin^2θ - 4sinθ

as cos^2θ = (1-sin^2θ)

4(1 - sin^2θ) = 4 + sin^2θ - 4sinθ

=> 4 - 4sin^2θ = 4 + sin^2θ - 4sinθ

adding - 4 + 4sin^2θ both side , we get

=> 0 = 5sin^2θ - 4sinθ

=> sinθ (5sinθ - 4 ) = 0

=> 5sinθ - 4 = 0

=> sinθ = 4/5

=> sinθ = sin53° [ °•° sin53° = 4/5 ]

=> θ = 53°

So, cos53° = 3/5

Hence, cosθ = 3/5



【 Hope it helps you 】