prove that $\tan(\alpha+\beta) = 2ac/(a^2-c^2)$ [duplicate]

trigonometry algebra-precalculus

HINT:

$$b\sec\theta=c-a\tan\theta$$

Squaring we get $$(c-a\tan\theta)^2=(b\sec\theta)^2=b^2(1+\tan^2\theta)$$

Rearrange to form a quadratic equation in $\tan\theta$ whose roots will be $\tan\alpha,\tan\beta$

Now Vieta's formula and expand $\tan(\alpha+\beta)$

Related

Global Trivialization of $M\oplus M$
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n [duplicate]
Cauchy Problem for inviscid Burgers' equation
Problem when $x=\cos (a) +i\sin(a),\ y=\cos (b) +i\sin(b),\ z=\cos (c) +i\sin(c),\ x+y+z=0$
Why do we say the harmonic series is divergent? [duplicate]
Squares, Cubes and Prime numbers
Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous? [duplicate]
WLOG means losing generality?
Prove the inequalities $1-\frac{x^2}{2}\le \cos(x)\le1-\frac{x^2}{2}+\frac{x^4}{24}$ [closed]
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$ [duplicate]
Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.