Question

Find the value of:
(3tan41°/cot49°)^2-(sin35°•sec55°/tan10°tan20°tan60°tan70°tan80°)^2

Answer 1

Answer:

26/3

Step-by-step explanation:

Find the value of:

(3tan41°/cot49°)^2-(sin35°•sec55°/tan10°tan20°tan60°tan70°tan80°)^2

(3tan41°/cot49°)²- (sin35°•sec55°/tan10°tan20°tan60°tan70°tan80°)²

Cot(90°-x°) = tanx° => Cot49° = Cot(90° - 41°) = tan41°

=  (3tan41°/tan41°)² - (sin35°•sec55°/tan10°tan20°tan60°tan70°tan80°)²

Similarly tan(90°-x°) = Cotx° = 1/tanx°

tan70° = Cot20° = 1/Tan20°  & tan80° = Cot10° = 1/Tan10°

Sec55° = 1/Cos55° = 1/Sin(90°-55°) = 1/Sin35°

= 3² - ((sin35°/sin35°)/((tan10°tan20°tan60°)/(tan20°tan10°)) )²

= 9 - (1/tan60°)²

=9 - (1/√3)²    ( tan 60° = √3)

= 9 - 1/3

= 26/3