Correct Answer - Option 1 : 25/12
Given
tan 12° + tan 22° - cot 78° - cot 68° + sin260° + sec230°
Formula used
tan(90° - A) = cot A
sin 60° = (√3/2)
sec 30° = 2/√3
Calculation
tan(90° - 78°) + tan(90° - 68°) - cot 78° - cot 68° + sin260° + sec230°
⇒ cot 78°+ cot 68° - cot 78° - cot 68° + (√3/2)2 + (2/√3)2
⇒ (3/4) + (4/3)
⇒ (9 + 16)/12
⇒ 25/12
∴ Value of tan 12° + tan 22° - cot 78°- cot 68° + sin260° + sec230° is 25/12
