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