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# Of sin A=5/13 the evaluate 5 sin A- 2 cos A divided by tan A

Soumendu Majumdar
159 Points
2 years ago
Dear Student,
The question doesn't clearly state what is being divided by tan A, still, I’ll try to solve it by dividing only  2cos A by tan A & the whole expression by tan A
Now
if only 2 cos A is being divided by tan A then it is $2 cos^2A/sinA$
now by Pythagorean triplets, we know  $5^2 + 12^2 = 13^2$
so cos A = $12/13$
so  $cos^2 A = 144/169$
Hence $5 sin A - 2cos^2A/sinA = 25/13 - 288/65 = - 163/65$
Now if the whole expression is divided by tan A, then
the expression becomes
$5 cos A - 2cos^2A/sinA$
$60/13 - 288/65 = 12/65$
Hope it helps!