Amazing Trigonometry_2

Geometry Level 3

If A + B + C = π A+B+C=\pi and cos ⁡ A = cos ⁡ θ sin ⁡ ϕ \cos { A } =\cos { \theta } \sin { \phi } , cos ⁡ B = cos ⁡ ϕ sin ⁡ Ψ \cos { B } =\cos { \phi } \sin { \Psi } , cos ⁡ C = cos ⁡ Ψ sin ⁡ θ \cos { C } =\cos { \Psi } \sin { \theta } , then find the value of tan ⁡ θ tan ⁡ ϕ tan ⁡ Ψ \tan { \theta } \tan { \phi } \tan { \Psi } .

This problem is a part of this set


The answer is 1.

Manish Dash by Manish Dash , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

L e t A = B = C = π 3 E a s i l y f i n d t h a t θ = ϕ = Ψ = π 4 tan ⁡ θ tan ⁡ ϕ tan ⁡ ψ = 1 Let\quad A=B=C=\frac { \pi }{ 3 } \\ Easily\quad find\quad that\quad \theta =\phi =\Psi =\frac { \pi }{ 4 } \\ \tan { \theta } \tan { \phi } \tan { \psi } =1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...