Question

If sinα=3/5, then the value of expression tanαsinα−cosαtanαsinα−cosα may be :​

Answer 1

Answer:

-0.71 or -71/100

Explanation:

Since sin alpha = 3/5,

height = 3x and hypotenuse = 5x

From Pythagoras Theorem,

height² + base² = hypotenuse²

base² = 25x² - 9x²

base² = 16x²

ergo, base = 4x

cos alpha = base/hypotenuse = 4/5

tan alpha = height/base = 3/4

tan alpha*sin alpha - cos alpha*tan alpha* sin alpha - cos alpha

= 3/4*3/5 - 4/5*3/4*3/5 - 4/5

= 9/20 - 9/25 - 4/5

= (45-36-80) / 100

= -71 / 100 (-0.71)