A geometry problem by Bala vidyadharan

Geometry Level 4

sin ⁡ θ cos ⁡ 3 θ + sin ⁡ 3 θ cos ⁡ 9 θ + sin ⁡ 9 θ cos ⁡ 27 θ \large \dfrac { \sin\theta }{ \cos3\theta } +\dfrac { \sin3\theta }{ \cos9\theta } +\dfrac { \sin9\theta }{ \cos27\theta }

If x + tan ⁡ θ = tan ⁡ 27 θ x+\tan\theta =\tan27\theta then state the expression above in terms of x x .

x 3 \frac x3 2 x 2x 3 x 3x x 2 \frac x2

View wiki
Bala Vidyadharan by Bala vidyadharan , 20, 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

Kushal Dey
Apr 14, 2020

sinx/cos3x=1/2 sin2x/(cosxcos3x) =1/2 (sin(3x-x))/(cosxcos3x) =1/2*(tan3x-tanx). Using this identity, by telescopic summation, the sum is, x/2.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...