Question

If cos A - 3 sinA = -1 and A is an acute angle; then the value of sin A is?

• A. 3/5
• B. 3/4
• C. 4/3
• D. 5/3
• E. 4/5

Answer 1

The correct option is A

3/5

cos A - 3 sinA = -1

$\begin{array}{c}\Rightarrow cosA+1=3sinA\\ Squaringbothsides\\ \Rightarrow co{s}^{2}A+1+2cosA=9si{n}^{2}A\\ \Rightarrow co{s}^{2}A+2cosA+1=9-9co{s}^{2}A\\ \Rightarrow 10co{s}^{2}A+2cosA-8=0\\ \Rightarrow 5co{s}^{2}A+cosA-4=0\\ \Rightarrow 5co{s}^{2}A+5cosA-4cosA-4=0\\ \Rightarrow \left(5cosA-4\right)(cosA+1)=0\\ \Rightarrow cosA=4/5orcosA=-1\\ ButcosA=-1isnotpossibleifAisanacuteangle.\\ SocosA=4/5.\\ Therefore,sinA=3/5.\end{array}$