Question

hii.. can u answer this question..

sin theta + 2 cos theta =1 given

to prove 2sin theta -cos theta =2​

Answer 1

As sin + 2cos = 1

By squaring

sin² + 4cos² + 4 *sin * cos =1

(1-cos²) + 4* (1- sin²) + 4* sin * cos = 1

1 - cos² + 4 - 4* sin² + 4* sin * cos = 1

By multiplying both sides by -1, we get

cos² - 4 + 4* sin² - 4 * sin * cos = 0

cos² + 4* sin² - 4* sin * cos = 4

(2 * sin - cos )² = (2)²

Square root both the side

Therefore 2sin - cos = 2

(proved)

Hope this helps you :)

Answer 2

sin + 2 cos = 1

sin + cos + cos = 1

sin + cos = 1 - cos

Now squaring

( sin + cos)^2 = ( 1 - cos)^2

Sin^2 + cos^2 + 2 sin cos = 1 + cos^2 - 2cos


sin^2 + 2 sin cos = 1 - 2cos

Take sin^2 = 1 - cos^2

So 1 - cos^2 + 2 sin cos = 1 - 2 cos

- cos^2 + 2 sin cos = - 2cos


- cos^2 + 2 cos + 2 sin cos = 0

cos ( - cos + 2 + 2 sin ) = 0

cos = 0 or 2 sin - cos = -2

So if cos = 0

then angle = 90

which is true

hence 2 sin - cos = 2 sin 90 - cos 90 = 2