Question

in the given figure ABC is a right angle triangle at C and D is the midpoint of BC.show that Tanteta/tanteta=1/2

Answer 1

tantheta=AC/BC ------1
tan phi= AC/DC -------2
:-tan thete/tan phi= DC/BC (divide 1&2)
=DC/(BD+DC)
= DC/2DC (BD=DC)
= 1/2

Answer 2

Answer:

Hence proved

$\frac{tan\theta}{tan\phi} = \frac{1}{2}$

Step-by-step explanation:

Given that

ΔABC is a right triangle and ∠C is 90°.

Since D is midpoint of BC, so

$DC = \frac{BC}{2}$

Lets consider the ΔABC, as we know

$tan\theta = \frac{Perp}{base}$

$tan\theta = \frac{AC}{BC}$ .... (1

also consider the ΔADC, as we know

$tan\phi = \frac{Perp}{base}$

$tan\phi = \frac{AC}{DC}$ .... (2

dividing equation 1 by equation 2

$\frac{tan\theta}{tan\phi} = \frac{\frac{AC}{BC}}{\frac{AC}{DC}}$

$\frac{tan\theta}{tan\phi} = \frac{DC}{BC}$

subtitute $DC =\frac{BC}{2}$ into the above equation

$\frac{tan\theta}{tan\phi} =\frac{\frac{BC}{2}}{BC}$

which can be simplified into

$\frac{tan\theta}{tan\phi}=\frac{1}{2}$

Hence proved