Question

Cot 9 degree cot 27 degree cot 45 degree cot 63 degree cot 81 degree equals 1

Answer 1

Answer:

now see the given terms

cot 9 can be paired with cot 81 because 81+9=90. they form a complimentary angle pair. so cot 81 can be rewritten as tan 9. so cot 9 ×tan9 value will be 1

similarly if we seperatw all complimentary angle pairs we will get the answer.

cot 63 and cot 27 is the second pair which will give 1 when multiplied.

then comes cot 45 whose value we already know to be 1

so 1×1×1=1

Answer 2

$\huge{\underline{\underline{\mathfrak{\pink{Solution}}}}}$

→ Cot 9° . Cot 27° . Cot 45° . Cot 63° . Cot 81 ° = 1 .

Taking LHS

→ Cot 9 . Cot 27° . Cot 45° . Cot 63° . Cot 81 °

→ (Cot 9° . Cot 81°). ( Cot 27° . Cot 63°) . (Cot 45° )

☆ Cot 45° = 1

☆ Cot $\theta$ = tan ( 90 - $\theta$)

Cot 81° = tan ( 90°-81°) = tan 9°

Cot 63° = tan( 90° - 63°) = tan 27°

→ (Cot 9° . tan9° ). (Cot 27° . tan 27° ). 1

☆ tan a × cot a = 1

→ 1×1×1

→ LHS = 1 = RHS

$<marquee>hope it helps$