If tan 25- a then the value of tan 205-tan 115-tan 245-tan 335- in terms of -a- is

Tan205 tan115^∘/tan245^∘+tan335^∘ =tan(180^∘+25^∘) tan(90^∘+25^∘)/tan(270^∘ 25^∘)+tan(360^∘ 25^∘) =tan25^∘ ( cot25^∘)/cot25^∘+tan25^∘ =a+1/a/1/a a =a^2+1/a/1+a^ ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

If tan 25∘= a...

Question

If $t a n 25^{\circ} = a t h e n t h e v a l u e o f \frac{t a n 205^{\circ} - t a n 115^{\circ}}{t a n 245^{\circ} + t a n 335^{\circ}}$ in terms of 'a' is_______

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Solution

$\frac{t a n 205 - t a n 115^{\circ}}{t a n 245^{\circ} + t a n 335^{\circ}}$
$= \frac{t a n (180^{\circ} + 25^{\circ}) - t a n (90^{\circ} + 25^{\circ})}{t a n (270^{\circ} - 25^{\circ}) + t a n (360^{\circ} - 25^{\circ})}$
$= \frac{t a n 25^{\circ} - (- c o t 25^{\circ})}{c o t 25^{\circ} + t a n 25^{\circ}}$
$= \frac{a + \frac{1}{a}}{\frac{1}{a} - a}$
$= \frac{\frac{a^{2} + 1}{a}}{\frac{1 + a^{2}}{a}}$
$= \frac{1 + a^{2}}{1 + a^{2}}$
=1

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If tan25∘=a then the value of tan205∘−tan115∘tan245∘+tan335∘ in terms of 'a' is_______

tan205−tan115∘tan245∘+tan335∘ =tan(180∘+25∘)−tan(90∘+25∘)tan(270∘−25∘)+tan(360∘−25∘) =tan25∘−(−cot25∘)cot25∘+tan25∘ =a+1a1a−a =a2+1a1+a2a =1+a21+a2 =1

If $t a n 25^{\circ} = a t h e n t h e v a l u e o f \frac{t a n 205^{\circ} - t a n 115^{\circ}}{t a n 245^{\circ} + t a n 335^{\circ}}$ in terms of 'a' is_______