The value of (tan 13ᵒ tan 36ᵒ tan 45ᵒ tan 54ᵒ tan 77ᵒ)/(2 sec² 60ᵒ (sin² 60ᵒ - 3 cos 60ᵒ +2)) is:

The value of (tan 13ᵒ tan 36ᵒ tan 45ᵒ tan 54ᵒ tan 77ᵒ)/(2…

The value of $\frac{tan 13^o tan 36^o tan 45^o tan 54^o tan 77^o}{2 sec^2 60^o (sin^2 60^o - 3 cos 60^o +2)}$ is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $\frac{1}{10}$

= $\frac{tan 13^o tan 36^o tan 45^o tan 54^o tan 77^o}{2 sec^2 60^o (sin^2 60^o - 3 cos 60^o +2)}$

= (tan13 × tan36 × tan45 × cot36 × cot13)/[2 × 4(3/4 - 3/2 + 2)]

= 1/(8(5/4)

= 1/10.