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Question
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
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Solution
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.
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