Question

Cos70 / sin20 + cos55 cosec35 / tan5 tan25 tan45 tan65 tan85 how to "solve"

Answer 1

Hope this will help you

Answer 2

Answer:

Following are the Steps to solve given expression:

Consider,

$\frac{cos\,70}{sin\,20}+\frac{cos\,55\;cosec\,35}{tan\,5\:tan\,25\:tan\,45\;tan\,65\;tan\,85}$

Step 1: First rewrite 70 = 90 - 20 , 55 = 90 - 35 , 5 = 90 - 85 and

           25 = 90 - 65

$\implies\frac{cos\,(90-20)}{sin\,20}+\frac{cos\,(90-35)\;cosec\,35}{tan\,(90-85)\:tan\,(90-65)\:tan\,45\;tan\,65\;tan\,85}$

Step 2: Use complimentary angle .i.e, cos(90° -x) = sin x and

            tan(90°-x) = cot x

$\implies\frac{sin\,20}{sin\,20}+\frac{sin\,35\;cosec\,35}{cot\,85\:cott\,65\:tan\,45\;tan\,65\;tan\,85}$

Step 3: Use result, sin x cosec x = 1 and tan x cot x = 1

$\implies\frac{1}{1}+\frac{1}{1\times1\times\:tan\,45}$

Step 4: use value of tan 45 = 1

$\implies\frac{1}{1}+\frac{1}{1\times1\times1}$

Step 5:  simplify

⇒ 1 + 1 = 2