Question

Write the value of tan 10° tan 15° tan 75° tan 80°?

Answer 1

SOLUTION :  

Given : tan 10° tan 15° tan 75° tan 80°

tan 10° tan 15° tan 75° tan 80°

= tan (90° - 80°) tan (90° - 75°) tan 75° tan 80°

= cot 80° cot 75° tan 75° tan 80°

[tan (90 - θ)  = cot θ ]

= (cot 75° tan 75° ) (cot 80° tan 80°)

= 1 × 1  = 1

[tan θ × cot θ = 1]

tan 10° tan 15° tan 75° tan 80° = 1  

Hence, the value of tan 10° tan 15° tan 75° tan 80° is 1.

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Answer 2

Solution :

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i ) tan ( 90 - A ) = cotA

ii ) tanA × cotA = 1

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Now ,

Value of

tan 10° tan 15° tan 75° tan 80°

Rearranging the terms , we get

= tan 10° tan 80° tan15° tan 75°

= tan 10 tan(90-10) tan 15 tan(90-15)

= ( tan 10°cot 10°)( tan 15°cot 15°)

= 1 × 1

= 1

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