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

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Q. If $tan 25^{\text{o}} = a ,$ then the value of $\frac{tan 205^{o} - tan ⁡ 115^{o}}{tan ⁡ 245^{o} + tan ⁡ 335^{o}}$ in terms of $a$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{tan 205^{o} - tan ⁡ 115^{o}}{tan ⁡ 245^{o} + tan ⁡ 335^{o}}=\frac{tan ⁡ 25^{o} + cot ⁡ 25^{o}}{cot ⁡ 25^{o} - tan ⁡ 25^{o}}$
$=\frac{tan^{2} 25^{o} + 1}{1 - tan^{2} ⁡ 25^{o}}=\frac{a^{2} + 1}{1 - a^{2}}$
$=\frac{1 + a^{2}}{1 - a^{2}}$