Evaluate

E. tan 26° tan 64°

By trigonometric identities, we can say

tan (90° - θ) = cot θ

And tan θ = 1/cot θ

Replace θ by 64°.

We get

tan (90° - 64°) = cot 64°

⇒ tan 26° = cot 64° [∵, 90° - 64° = 26°]

And tan 64° = 1/cot 64°

Using these values, we can solve for the given expression.

tan 26° tan 64° = cot 64° tan 64°

⇒ tan 26° tan 64° = cot 64°/cot 64°

⇒ tan 26° tan 64° = 1