Question

Question #c86cf

Answer 1

I'll solve `59ii`.

You will need the following identities to solve this equation:

`sin2theta = 2sinthetacostheta`

`cos2theta = 1 - 2sin^2theta`

Explanation:

`(2sinthetacostheta)/(2sintheta) - costheta(1 - 2sin^2theta)= costheta`

`costheta - costheta - costheta(1 - 2sin^2theta) = 0`

`-costheta = 0 and sin^2theta = 1/2`

`-costheta = 0 and sintheta =+- 1/sqrt(2)`

`theta = 90^@, 270^@, 45^@, 135^@, 225^@ and 315^@`

Hopefully this helps!

Answer 2

Item 60. See demonstration.

Explanation:

Item 60

`tan(30^@)=h/(bar (BC))`
`tan(45^@)=h/(bar(CA))`
`(bar (BC))^2+(bar(CA))^2=(2r)^2` (mind that `angle C = 90^@`)

then

`(h/(tan(30^@)))^2+(h/(tan(45^@)))^2 = h^2(cot(30^@)^2+cot(45^@)^2)= 4 r^2`

but

`(cot(30^@)^2+cot(45^@)^2) = 4`

then

`r = h`