Question

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

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

Answer 1

The correct option is B $\pm 3$

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

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

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

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

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

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

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