If 4 sec a _ 5 = 0, evaluate 2 cos a + 5 sin a ÷ 2 sin a + 5 cos a

23/26 = 0.8846=0.88 [ to the nearest hundredth]

Step-by-step explanation:

4 sec a-5 = 0; seca=1/cos a

Therefore;

4 sec a-5 = 0=>4/cos a - 5 = 0

Multiplying through by cos a, we have;

4-5cosa= 0=>4= 5cosa

4/5 = cosa

a = cos^{-1}0.8

=36.88

Alternatively Cos a =4/5

Sina = 3/5; {note Cos a = adjacent / hypothesis and from Pythagoras rule we can derive the value of the opposite side which is;

5^2 -4^2 = 25-16 = 9; hence the opposite side is √9 = 3;sin a = opposite/ hypothenus = 3/5}

Substituting the value of Cosa and Sina into the expression below;

2 cos a + 5 sin a ÷ 2 sin a + 5 cos a

We have ;

[2×4/5 + 5× 3/5 ]/ [2 × 3/5 + 5× 4/5]

[8/5 + 15/5 ]/ [6/5 + 20/5]

[23/5]/[26/5] = 23/5 × 5/26 = 23/26

=