If tan 25 texto = a , then the value of (tan 205o - tan â¡ 115o/tan â¡ 245o + tan â¡ 335o) in terms of a is

Question

If tan 25 texto = a , then the value of (tan 205o - tan â¡ 115o/tan â¡ 245o + tan â¡ 335o) in terms of a is (A) (1 - a2/1 + a2) (B) (1 - a/2 a) (C) (2 a/1 + a2) (D) (1 + a2/1 - a2)

Tardigrade Admin · Accepted Answer

(tan 205o - tan â¡ 115o/tan â¡ 245o + tan â¡ 335o)=(tan â¡ 25o + cot â¡ 25o/cot â¡ 25o - tan â¡ 25o) =(tan2 25o + 1/1 - tan2 â¡ 25o)=(a2 + 1/1 - a2) =(1 + a2/1 - a2)

Q. If $t an 2 5^{o} = a,$ then the value of $\frac{t an 20 5 ^{o} - t an 11 5 ^{o}}{t an 24 5 ^{o} + t an 33 5 ^{o}}$ in terms of $a$ is

$\frac{1 - a ^{2}}{1 + a ^{2}}$

$\frac{1 - a}{2 a}$

$\frac{2 a}{1 + a ^{2}}$

$\frac{1 + a ^{2}}{1 - a ^{2}}$

$\frac{t an 20 5 ^{o} - t an 11 5 ^{o}}{t an 24 5 ^{o} + t an 33 5 ^{o}} = \frac{t an 2 5 ^{o} + co t 2 5 ^{o}}{co t 2 5 ^{o} - t an 2 5 ^{o}}$
$= \frac{t a n ^{2} 2 5 ^{o} + 1}{1 - t a n ^{2} 2 5 ^{o}} = \frac{a ^{2} + 1}{1 - a ^{2}}$
$= \frac{1 + a ^{2}}{1 - a ^{2}}$

Q. If tan25o=a, then the value of tan⁡245o+tan⁡335otan205o−tan⁡115o​ in terms of a is

1+a21−a2​

2a1−a​

1+a22a​

1−a21+a2​