Question

Hii frnds

slove this

Answer 1

⭐Hey there!!

Given that : 3sinA + 5cosA = 5 -----------------(1)

Let 5sinA - 3cosA = x ---------------------(2)

Squaring both equation and add them : we get,

=> 9sin²A + 25cos²A +30sinA. cosA = 25 :{1}

=> 25sin²A + 9cos²A - 30sinA. cosA = x² :{2}

Add____________________________

= 9(sin²A + cos²A) + 25(sin²A + cos²A) = x² + 25

#here we know that : Sin²A + Cos²A = 1

Now put the value in above equation :

=>>> 9×1 + 25×1 = x² + 25

=> 9 + 25 = x² + 25

=> x² = 9

=> x = +_ 3

So we consider x = 5sinA - 3cos A...

• 5sinA - 3cosA = +_ 3 [proved]

_______________________________________
⭐hope it will help u

Answer 2

(ii) Given Equation is 3sinA + 5cosA = 5

On Squaring both sides, we get

= > (3 sinA + 5 cosA)^2 = (5)^2

= > 9 sin^2A + 25cos^2A + 30sinAcosA = 25

= > 9(1 - cos^2A) + 25(1 - sin^2A) + 30sinAcosA  = 25

= > 9 - 9cos^2A + 25 - 25sin^2A + 30sinAcosA = 25

= > -9cos^2A - 25sin^2A + 30sinAcosA = 25 - 34

= > -9cos^2A - 25sin^2A + 30sinAcosA = -9

= > 9cos^2A + 25sin^2A - 30sinAcosA = 9

= > (5sinA - 3cosA)^2 = 9

$= \ \textgreater \boxed{5sinA-3cosA = +3, -3}$


Hope this helps!