Question

Without using trignometric table evaluate (cos 58 / sin 32 ) + (sin 22 / cos 68) - cos 38 cosec 52 / tan 18 . tan 25 tan 60 tan 72 tan 55

Everything in deg ..pls answer

Answer 1

Answer:

Value of Given Expression is $\frac{2\sqrt{3}-1}{\sqrt{3}}$

Step-by-step explanation:

Given: Expression

$\frac{cos\,58^{\circ}}{sin\,32^{\circ}}+\frac{sin\,22^{\circ}}{cos\,68^{\circ}}-\frac{cos\,38^{\circ}\:\:cosec\,52^{\circ}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:tan\,72^{\circ}\:tan\,65^{\circ}}$

we use Complimentary angles to simplify .i.e.,

$sin\,x=cos(90-x)\:\:,\:\:cos\,x=sin(90-x)\:\: and\:\:tan\,x=cot(90-x)$

using this in given expression we get,

$\frac{cos\,58^{\circ}}{cos\,(90-32)^{\circ}}+\frac{sin\,22^{\circ}}{sin\,(90-68)^{\circ}}-\frac{cos\,38^{\circ}\times\frac{1}{sin\,52^{\circ}}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:cot\,(90-72)^{\circ}\:cot\,(90-65)^{\circ}}$

$\implies\frac{cos\,58^{\circ}}{cos\,58^{\circ}}+\frac{sin\,22^{\circ}}{sin\,22^{\circ}}-\frac{cos\,38^{\circ}\times\frac{1}{cos\,(90-52)^{\circ}}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:cot\,18^{\circ}\:cot\,25^{\circ}}$

$\implies1+1-\frac{cos\,38^{\circ}\times\frac{1}{cos\,38^{\circ}}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:\times\frac{1}{tan\,18^{\circ}}\times\frac{1}{tan\,25^{\circ}}}$

$\implies1+1-\frac{1}{1\times\:tan\,60^{\circ}\:\times1}}$

$\implies1+1-\frac{1}{tan\,60^{\circ}}}$

$\implies2-\frac{1}{\sqrt{3}}$  ( ∵ $tan\,60^{\circ}=\sqrt{3}$ )

$\implies\frac{2\sqrt{3}-1}{\sqrt{3}}$

Therefore, Value of Given Expression is $\frac{2\sqrt{3}-1}{\sqrt{3}}$

Answer 2

Hope you understood.

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