Question

in a figure AD=BD, angle B=90° and angle BCD= theta , then cos theta equal to​

Answer 1

Answer:

Step-by-step explanation:

Given: In triangle ABC, <B = 90 deg. BD is such that <DBC = <BCD.

To prove that AD = BD.

Proof: In triangle BCD, <BCD = <CBD = <C.

So BCD is an isosceles triangle.

Now, <ABD = 90 - <C.

In triangle ABD, <ADB = <BCD + <CBD = 2<C.

But, <BAD + <ABD + <ADB = 180, or

<BAD + (90 - <C) + 2<C = 180, or

<BAD = 180 - (90 - <C) - 2<C = 90 - C = <ABD.

Therefore ABD is an isosceles triangle, and so AD = BD.

QED.