PR2=PQ2+QR2⇒132=52+QR2⇒169=25+QR2⇒QR2=169−25=144⇒QR=√144=12
Therefore, the adjacent side QR=12.
We know that, in a right angled triangle,
cosθ is equal to adjacent side over hypotenuse that is cosθ=AdjacentsideHypotenuse and
tanθ is equal to opposite side over adjacent side that is tanθ=OppositesideAdjacentside
Here, we have opposite side PQ=5, adjacent side QR=12 and the hypotenuse PR=13, therefore, the trignometric ratios of angle A can be determined as follows:
cosA=AdjacentsideHypotenuse=QRPR=1213
tanθ=OppositesideAdjacentside=PQQR=512
Now, we find
5sinA−2cosAtanA=(5×513)−(2×1213)512=2513−2413512=113512=113×125=1265
Hence, 5sinA−2cosAtanA=1265.