If tan (A+B)=p, tan (A-B)=q, then the value of tan 2A is

Question

If tan (A+B)=p, tan (A-B)=q, then the value of tan 2A is (A)  (p+q/p-q)  (B)  (p-q/1+pq)  (C)  (1+pq/1-p)  (D)  (p+q/1-pq)

Tardigrade Admin · Accepted Answer

Let A= undersetx→ ∞ mathop lim x1/x Taking log on both sides, we get log A= undersetx→ ∞ mathop lim (1/x) log x ⇒ log A=0 ( ∵ undersetx→ ∞ mathop lim ( log x/xm)=0 ∀ m>0 ) ⇒ A=e0=1 ⇒ undersetx→ ∞ mathop lim x1/x=1

Q. If $tan (A + B) = p, tan (A - B) = q,$ then the value of tan 2A is

$\frac{p + q}{p - q}$

$\frac{p - q}{1 + pq}$

$\frac{1 + pq}{1 - p}$

$\frac{p + q}{1 - pq}$

Let $A = x \to \infty lim x^{1/ x}$ Taking log on both sides, we get $lo g A = x \to \infty lim \frac{1}{x} lo g x$ $\Rightarrow$ $lo g A = 0$ $(∵ x \to \infty lim \frac{l o g x}{x ^{m}} = 0 \forall m > 0)$ $\Rightarrow$ $A = e^{0} = 1$ $\Rightarrow$ $x \to \infty lim x^{1/ x} = 1$

Q. If tan(A+B)=p,tan(A−B)=q, then the value of tan 2A is

p−qp+q​

1+pqp−q​

1−p1+pq​

1−pqp+q​