Question

8. ( (1) 2 sin alpha+15 cos ^{2} alpha=7 )
( Rightarrow 2 sin alpha+15left(1-sin ^{2} alpharight)=7 )
( Rightarrow 2 sin alpha+15-15 sin ^{2} alpha=7 )
( Rightarrow 15 sin ^{2} alpha-2 sin ^{2} alpha-8=0 )
( Rightarrow 15 sin ^{2} alpha-12 sin alpha+10 sin )
( alpha-8=0 )
( Rightarrow 3 sin alpha(5 sin alpha-4)+2(5 )
( sin alpha-4)=0 )
( Rightarrow(3 sin alpha+2)(5 sin alpha-4)=0 )
( Rightarrow 5 sin alpha-4=0 )
( Rightarrow sin alpha=frac{4}{5} )
( therefore operatorname{cosec} alpha=frac{5}{4} )
( cot alpha=sqrt{operatorname{cosec}^{2} alpha-1} )
( =sqrt{frac{25}{16}-1}=sqrt{frac{9}{16}}=frac{3}{4} )

# 8. If a is a positive acute angle and 2sina + 15cos'a = 7, then the value of cota is: polo

Solution