1- cosx7. tan10

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Solution

The given function is tan −1 ( 1−cosx 1+cosx ) , x<π.

Simplify the given function,

tan −1 ( 1−cosx 1+cosx )= tan −1 ( 2 sin 2 x 2 2 cos 2 x 2 ) = tan −1 ( sin x 2 cos x 2 ) = tan −1 ( tan x 2 ) = x 2

Therefore, the simplest form of the given function is x 2 .

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Similar questions

L = (4 tan 1^{\circ}) (4 tan 2^{\circ}) (4 tan 3^{\circ}) \dots (4 tan 10^{\circ}),

M = (tan 2^{\circ}) (tan 4^{\circ}) (tan 6^{\circ}) \dots (tan 20^{\circ}),

N = (1 + tan 1^{\circ}) (1 - tan 1^{\circ}) (1 + tan 2^{\circ}) (1 - tan 2^{\circ}) \dots (1 + tan 10^{\circ}) (1 - tan 10^{\circ})

\frac{L}{128 M N}

$tan 10^{\circ} tan 15^{\circ} tan 75^{\circ} tan 80^{\circ} = ?$
(a) $3$
(b) $13$
(c) $- 1$
(d) $1$

tan 10^{o} tan 15^{o} tan 75^{o} tan 80^{o} = 1

(\sqrt{3} + t a n 1^{0}) .

(1 + tan 5^{\circ}) (1 + tan 10^{\circ}) (1 + tan 15^{\circ}) . . . (1 + tan 45^{\circ}) = 2^{k}

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