Question

If $3sin\theta +5cos\theta =5$, then the value of $5sin\theta -3cos\theta =?$

• A. $\pm 4$
• B. $\pm 3$
• C. $\pm 5$
• D. $\pm 2$

Answer 1

Answer: (B)

$\pm 3$

If $3sin\theta +5cos\theta =5$, then

$=>3sin\theta +5cos\theta =5$

$=>(3sin\theta +5cos\theta {)}^2=25$

$=>9si{n}^2\theta +25co{s}^2\theta +30sin\theta cos\theta =25$

$=>9(1-co{s}^2\theta )+25(1-si{n}^2\theta )+30sin\theta cos\theta =25$

$=>25si{n}^2\theta +9co{s}^2\theta -2\times 5sin\theta 3cos\theta =9$

$=>(5sin\theta -cos\theta {)}^2=9$

$=>5sin\theta -cos\theta =\pm 3$

Hence, option 'B' is correct.