1. ## Difficult Trigo Problems

Hello people,

1) If $\displaystyle Cos(a) + Cos(b) + Cos(c) = Sin(a) + Sin(b) + Sin(c) = 0$,
then the value of $\displaystyle Cos(3a) + Cos(3b) + Cos(3c)$ = ?

2) If [e^cos(x)] - [e^-cos(x)] = 4. Find the value of $\displaystyle Cos(x)$

3) If $\displaystyle 2Sin^2 \theta$ = $\displaystyle 3 Cos \theta$, find the positive angle of $\displaystyle \theta$

4) In $\displaystyle \triangle ABC$, $\displaystyle \theta$ is an acute angle & $\displaystyle tan\theta$ is equal to three times of $\displaystyle Cot\theta$. Find the value of $\displaystyle (sin^2\theta) + (Cosec^2\theta) - (1/2) (Cot^2\theta)$

2. Originally Posted by saberteeth
Hello people,

1) If $\displaystyle Cos(a) + Cos(b) + Cos(c) = Sin(a) + Sin(b) + Sin(c) = 0$,
then the value of $\displaystyle Cos(3a) + Cos(3b) + Cos(3c)$ = ?

2) If [e^cos(x)] - [e^-cos(x)] = 4. Find the value of $\displaystyle Cos(x)$

3) If $\displaystyle 2Sin^2 \theta$ = $\displaystyle 3 Cos \theta$, find the positive angle of $\displaystyle \theta$

4) In $\displaystyle \triangle ABC$, $\displaystyle \theta$ is an acute angle & $\displaystyle tan\theta$ is equal to three times of $\displaystyle Cot\theta$. Find the value of $\displaystyle (sin^2\theta) + (Cosec^2\theta) - (1/2) (Cot^2\theta)$

$\displaystyle 2) e^{\cos x} - e^{-\cos x} = 4$

$\displaystyle e^{2\cos x } - 1 = 4 e^{\cos x}$

$\displaystyle e^{2\cos x } - 4e^{\cos x} - 1 =0$

let $\displaystyle u=e^{\cos x}$

$\displaystyle u^2 - 4u - 1=0$

$\displaystyle u=\frac{4 \mp \sqrt{16+4}}{2}$

$\displaystyle u=2+\sqrt{5}$ or $\displaystyle u =2-\sqrt{5}$

$\displaystyle e^{\cos x} = 2+\sqrt{5} \Rightarrow \cos x = \ln (2+\sqrt{5} )$

$\displaystyle e^{\cos x } = 2 -\sqrt{5} \Rightarrow \cos x = \ln (2-\sqrt{5})$

3)$\displaystyle 2\sin ^2 \theta = 3\cos \theta$

$\displaystyle 2(1-\cos ^2\theta) = 3\cos \theta$

$\displaystyle 2\cos ^2\theta +3\cos \theta -2=0$

let $\displaystyle u=\cos \theta$

$\displaystyle 2u^2+3u-2 =0$ you can solve it after you find u values find x

3. Originally Posted by saberteeth
Hello people,

1) If $\displaystyle Cos(a) + Cos(b) + Cos(c) = Sin(a) + Sin(b) + Sin(c) = 0$,
then the value of $\displaystyle Cos(3a) + Cos(3b) + Cos(3c)$ = ?

2) If [e^cos(x)] - [e^-cos(x)] = 4. Find the value of $\displaystyle Cos(x)$

3) If $\displaystyle 2Sin^2 \theta$ = $\displaystyle 3 Cos \theta$, find the positive angle of $\displaystyle \theta$

4) In $\displaystyle \triangle ABC$, $\displaystyle \theta$ is an acute angle & $\displaystyle tan\theta$ is equal to three times of $\displaystyle Cot\theta$. Find the value of $\displaystyle (sin^2\theta) + (Cosec^2\theta) - (1/2) (Cot^2\theta)$

$\displaystyle 4) \tan \theta = 3 \cos \theta$

$\displaystyle \tan \theta = \frac{3}{\tan \theta }$

$\displaystyle \tan ^2\theta = 3$

$\displaystyle \tan \theta = \sqrt{3}$ $\displaystyle \Rightarrow \theta =\frac{\pi}{3}$

the rest of question just you should know

$\displaystyle \sin \frac{\pi}{3} = ??$

$\displaystyle \sec \frac{\pi}{3}= ??$

$\displaystyle \cos \frac{\pi}{3} =??$
the rest for you