Question

If 3 sinA +5 cosA =5,prove that 5 sinA -3 cosA =+-3​

Answer 1

Step-by-step explanation:

sq on both sides

i.e.,

9sin^2A+25cos^2A=25...... to be eq 1

let+-3=k,then

25sin^2A-9cos^2A=k^2...... to be eq 2

add eq 1 and eq 2

=>9sin^2A+25sin^2A+25cos^2A-9cos^2A=25+k^2

=>25(sin^2A+cos^2A)+9(sin^2A+cos^2)=25+k^2

=>25(1)+9(sin^2A+cos^2A)=25+k^2

=>9(1)=k^2

=>k=rt(9)

=>k=+-3

hence proved...

note:sin^2A+cos^A=1