Question

tan 27° + cot 63° The value of is tan 27° (sin 25° + cos 65°) (SSC CPO 2013] (a) cosec 25° (b) 2 tan 27° (c) sin 25 (d) tan 65​

Answer 1

Answer:

Coss 25°

hope it's help you!!!

Answer 2

Given :   $\dfrac{\tan 27^{\circ}+\cot 63^{\circ}}{tan 27^{\circ}(\sin 25^{\circ}+\cos 65^{\circ})}$

To Find :   Value

(a) cosec 25°

(b) 2 tan 27°

(c) sin 25

(d) tan 65​

Solution:

$\dfrac{\tan 27^{\circ}+\cot 63^{\circ}}{\tan 27^{\circ}(\sin 25^{\circ}+\cos 65^{\circ})}$

tan x = cot (90° - x)

Sinx = cos(90° - x)

cot 63° = cot ( 90° - 27°)  = tan27°

cos 65° = cos ( 90° - 25°)  =sin 25°

$\dfrac{\tan 27^{\circ}+\cot 63^{\circ}}{\tan 27^{\circ}(\sin 25^{\circ}+\cos 65^{\circ})}$

$=\dfrac{\tan 27^{\circ}+\tan 27^{\circ}}{\tan 27^{\circ}(\sin 25^{\circ}+\sin 25^{\circ})}$

$=\dfrac{2\tan 27^{\circ}}{\tan 27^{\circ}(2\sin 25^{\circ})}$

$=\dfrac{1}{ \sin 25^{\circ}}$

= Cosec 25°

Correct option  is  option a)  Cosec 25°

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