Question

evaluate (3cos 55 deg \ 7sin 35 deg) - (4)(cos 70 deg cosec20 deg) \ (7)(tan5 deg tan 25 deg tan 45 deg tan 65 deg tan 85 deg)

Answer 1

that is your answer.....



 

 

Is this supposed to be: 

3cos(55°)/[7sin(35°)] - 4[cos(70°)csc(20°)]/[7tan(5°)tan(25°)tan...‡ 

If so, use: 

tan(90° - x) = cot(x) <==> cot(90° - x) = tan(x) 
sin(90° - x) = cos(x) <==> cos(90° - x) = sin(x). 

So we have: 

3cos(55°)/[7sin(35°)] 
=> 3sin(90° - 55°)/[7sin(35°)] 
= 3sin(35°)/[7sin(35°)] 
= 3/7. 

4 * [cos(70°)csc(20°)]/[7 * tan(5°) * tan(25°) * tan(45°) * tan(65°) * tan(85°)] 
=> (4/7)[cos(70°)/sin(20°)]/[tan(5°) * tan(25°) * tan(45°) * tan(65°) * tan(85°)] 
= (4/7)[sin(20°)/sin(20°)]/[tan(5°) * tan(25°) * tan(45°) * tan(65°) * tan(85°)] 
= (4/7)/[tan(5°) * tan(25°) * tan(45°) * tan(65°) * tan(85°)] 
= 4/[7 * tan(5°)tan(85°) * tan(25°)tan(65°) * tan(45°)] 
= 4/[7 * tan(5°)cot(5°) * tan(25°)cot(25°) * tan(45°)] 
= 4/(7 * 1 * 1 * 1) 
= 4/7. 

Thus, the expression equals 3/7 - 4/7 = -1/7. 

I hope this helps!