Question

sin+2cos=1
prove 2sin-cos=2

Answer 1

sinA+2cosA = 1
Squaring both sides
→ (sinA+2cosA)² = (1)²
→ sin²A+4cos²A+4sinAcosA = 1
→ 1-cos²A+4-4sin²A+4sinAcosA = 1
→ 4sin²A+cos²A-4sinAcosA = 4
→ (2sinA-cosA)² = (2)²
→ 2sinA-cosA = 2

Answer 2

hey friends ☺

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

2sin - cos =2 ---------2)

squaring both equation 1 , and 2, adding them.

then ..

(sin + 2 cos) ² + (2 sin - cos )²

=>sin² +2 ×2 sin×cos +4 cos²+ 4 sin² + cos² + 2 ×2sin×cos

=>sin² +cos². +4( sin² + cos² )

=>1 + 4

=>5 ------3

and again ...
squaring and adding both equation 1 ) and 2)
(sin + 2cos)²+(2sin + cos )²

=> 1 + (2sin+cos)² =5 { from 1 and 3}

=>(2sin + cos ) =√4

=>2sin + cos =2 Prooved

hope it helps you. .!!!

#rajukumar111