Question

if 4tan theta 3 prove that sin theta cos theta 12/25​

Answer 1

Step-by-step explanation:

$Given,\\4tan\theta=3\\\\tan\theta=\frac{3}{4} \\\\ from \ the \ triangle, \\ hypotenuse^2=side_1^2+side_2^2 \\ hyp^2=3^2+4^2\\hyp^2=9+16\\hyp^2=9+16\\hyp^2=25\\hyp=\sqrt{25}\\\boxed{hypotenuse=5} \\\\ => opposite \ side \ of \ angle \ \theta=3 \ units \\ adjacent \ side \ of \ angle \ \theta=4\ units\\\\ \rightarrow sin \theta=\frac{opp.side \ of \ angle}{hypotenuse}\\\\ \rightarrow sin\theta=\frac{3}{5}\\\\ \rightarrow cos\theta=\frac{adj.side \ of\ angle}{hypotenuse}\\\\ \rightarrow cos\theta=\frac{4}{5}$

$=> sin\theta \ cos\theta=(\frac{3}{5} ). (\frac{4}{5}) =\frac{12}{25} \\\\ hope \ it \ helps$