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Mathematics Question on Properties of Inverse Trigonometric Functions

tan⁡25?=p⇒ tan 245?+tan⁡ 335?tan⁡ 205?−tan⁡ 115?=\tan 25? = p \Rightarrow \: \frac{tan\, 245? + \tan\, 335? }{\tan\, 205? - \tan\, 115?} =

A

p2−1p2+1\frac{p^2 -1}{p^2 +1}

B

p2+1p2−1\frac{p^2 + 1 }{p^2 - 1}

C

1−p21+p2\frac{1 - p^2 }{1 + p^2 }

D

1+p21−p2\frac{ 1 + p^2 }{1 - p^2 }

Answer

1−p21+p2\frac{1 - p^2 }{1 + p^2 }

Explanation

Solution

tan⁡(245?)=tan⁡(270?−25?)\tan (245?) = \tan (270? - 25?) tan⁡(335?)=tan⁡(360?−25?)\tan (335?) = \tan (360? -25?) tan⁡(205?)=tan⁡(180?+25?)\tan (205?) = \tan (180? + 25?) tan⁡(115?)=tan⁡(90?+25?)\tan (115?) = \tan (90? + 25?)