Question

Prove the following:

If tan A = `3/4`, then sinA cosA = `12/25`

Answer 1

Given, tan A = `3/4 = "P"/"B" = "Perpendicular"/"Base"`

Let P = 3k and B = 4k

By Pythagoras theorem,

H² = P² + B²

= (3k)² + (4k)²

= 9k² + 16k²

= 25k²

⇒ H = 5k   ...[Since, side cannot be negative]

∴ sin A = `"P"/"H" = (3"k")/(5"k") = 3/5`

And cos A = `"B"/"H" = (4"k")/(5"k") = 4/5`

Now, sin A cos A = `3/5 * 4/5 = 12/25`

Hence proved.