Can ${tan 65}^{o} = {tan 25}^{o} + 2 {tan 40}^{o}$ ?
If yes answer is 1,else 0

True

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False

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Solution

The correct option is A True
$t a n 65 - t a n 40 = t a n 25 + t a n 40.$

$U s i n g t a n A - t a n B = \frac{s i n (A - B)}{c o s A c o s B} a n d t a n A + t a n B = \frac{s i n (A + B)}{c o s A c o s B}$

$S o t h a t, t o p r o v e \frac{s i n 25}{c o s 65. c o s 40} = \frac{s i n 65}{c o s 40 c o s 25}$

$s i n 65 = c o s (90 - 65)$ $= c o s 25$
$s i n 25 = s i n (90 - 65)$ $= s i n 65$

$⟹ 1 = 1$

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Similar questions

tan 65^{o} = tan 25^{o} + 2 tan 40^{o}

tan 65^{0} = tan 25^{0} + tan 40^{0}

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