Question

cos 70/sin 20 +cos 55.cosec35/tan 5.tan25.tan65.tan85=2​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Consider,

$\frac{cos\,70}{sin\,20}+\frac{cos\,55\times cosec\,35}{tan\,5\timestan\,25\times tan\,65\times tan\,85}$

use this $cosec\,\theta=\frac{1}{sin\,\theta}$

$=\frac{cos\,(90-20)}{sin\,20}+\frac{cos\,55\times\frac{1}{sin\,35}}{tan\,5\times tan\,25\times tan\,(90-25)\times tan\,(90-5)}$

use this, $cos\,(90-\theta)=sin\,\theta\:\:and\:\:tan\,(90-theta)=cot\,\theta$

$=\frac{sin\,20}{sin\,20}+\frac{cos\,(90-35)\times\frac{1}{sin\,35}}{tan\,5\times tan\,25\times cot\,25\times cot\,5}$

$=\frac{sin\,20}{sin\,20}+\frac{sin\,35\times\frac{1}{sin\,35}}{tan\,5\times tan\,25\times\frac{1}{tan\,25}\times\frac{1}{tan\,5}}$

$=\frac{1}{1}+\frac{1\times\frac{1}{1}}{1\times1\times\frac{1}{1}\times\frac{1}{1}}$

$=1+\frac{1}{1}$

$=1+1$

= 2

Hence Proved