Question

State whether the given statement is true or false

If $3\sin \theta +5\cos \theta =5$, then $5\sin \theta -3\cos \theta =\pm 2$.

• A. True
• B. False

Answer 1

The correct option is B False

Given,$3sin\theta +5cos\theta =5--->A$
let $5sin\theta -3cos\theta =x--->B$
On squaring both equations and adding each other,
$\Rightarrow (3sin\theta +5cos\theta {)}^2+(5sin\theta -3cos\theta {)}^2=25+x^2$
$\Rightarrow 9\ast (si{n}^2\theta +co{s}^2\theta )+25\ast (si{n}^2\theta +co{s}^2\theta )=25+x^2$
$\Rightarrow (9+25)=25+x^2$
$\Rightarrow x=\pm 3$