Question

Cot theta. Tan(90-theta)-sec(90-theta) cosec theta +√3 tan 12.tan60.tan78=2

Answer 1

let theta = A

According to the question,

cot A . tan (90 - A) - sec (90 - A) . cosecA + √3 . tan12 . tan60 . tan78 =2

LHS : cot A . tan (90 - A) - sec (90 - A) . cosecA + √3 . tan12 . tan60 . tan78

• cot A . cot A - cosec A . cosec A + √3 . tan (90 - 78) . 1/√3 . tan 78
• cot²A - cosec²A + cot 78 . tan78
• 1 + 1/tan 78 . tan78
• 1 + 1 = 2 = RHS

Hence Proved !

Answer 2

therefore the value is 2