Question

1. Show that:
tan 10° tan 15° tan 75º tan 80º = 1​

Answer 1

Answer:

Step-by-step explanation:

tan (90 - x) = cot x = 1 / tan x

tan (90 - 80) = tan 10 = 1 / tan 80

So tan 10 tan 80 = 1,

tan 15 tan75 = 1

Answer 2

Answer;

Prerequisites:

• Tan A = Cot ( 90 - A )
• Tan A * Cot A = 1

According to the question, we must prove that:

Tan 10° * Tan 15° * Tan 75° * Tan 80° = 1

Now using the first prerequisite we can say that,

Tan 10° = Cot ( 90 - 10 )°

Tan 10° = Cot 80°

Similarly,

Tan 15° = Cot ( 90 - 15 )°

Tan 15° = Cot 75°

Substituting in the equation we get,

Cot 80° * Cot 75° * Tan 75° * Tan 80°

From prerequisite we can say that,

Cot 80 * Tan 80 = 1

Cot 75 * Tan 75 = 1

Therefore in the left hand side we get the value as 1 * 1 which is 1

Hence LHS = RHS

Hence proved !!