Question

The value of tan 10° tan 15° tan 75° tan 80° is
(a) −1
(b)0
(c)1
(d) None of these

Answer 1

SOLUTION :  

The correct option is  (c)  : 1

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.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

$\huge \bf \pink{Hey \: there !! }$


▶ Question :-

→ The value of tan 10° tan 15° tan 75° tan 80° .


▶ Answer :-

→ Option C = 1 .

$\huge \orange{ \mid{ \underline{ \overline{ \sf Explanation :- }} \mid}}$


We have,

°•° tan 10° tan 15° tan 75° tan 80° .

[ We write this as :- ]

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

[ We know that :- tan( 90 - ∅ ) = cot ∅ ] .

= cot 80° cot 75° tan 75° tan 80° .

= cot 80° tan 80° cot 75° tan 75° .

[ We know that :- tan ∅ × cot ∅ = 1 ] .

= 1 × 1 .

$\huge \boxed{ \boxed{ \green{\underline{ \underline{ \sf = 1.}}}}}$



✔✔ Hence, it is solved ✅✅.


THANKS



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