Answer:
CosP +CosQ = [tex]\frac{7}{5}[/tex] .
Step-by-step explanation:
Given : In ΔPQR, ∠P and ∠Q are complimentary angles. If sinQ = 4/5 .
To find : cosP + cosQ =
Solution : We have given that ∠P and ∠Q are complimentary angles.
P + Q = 90 .
Q = 90 - P.
Then sin( 90 -p ) = [tex]\frac{4}{5}[/tex] .
As we know that sin( 90 -p ) = CosP = [tex]\frac{4}{5}[/tex] .
We have SinQ = [tex]\frac{4}{5}[/tex] .
CosQ =[tex]\sqrt{1 - Sin^{2}Q }[/tex]
Plugging the value of SinQ
CosQ = [tex]\sqrt{1 - (\frac{4}{5}) ^{2} }[/tex].
CosQ = [tex]\sqrt{1 - (\frac{16}{25})}[/tex].
CosQ =[tex]\sqrt{\frac{9}{25} }[/tex].
CosQ = [tex]\frac{3}{5}[/tex] .
CosP +CosQ = [tex]\frac{4}{5}[/tex] + [tex]\frac{3}{5}[/tex].
CosP +CosQ = [tex]\frac{7}{5}[/tex] .
Therefore, CosP +CosQ = [tex]\frac{7}{5}[/tex] .
