Question

Without using trigonometry tables, find the value of each of the expressions given below:

3cot31° tan15° cot27° tan75° cot63° cot59°​

Answer 1

Answer:

we know that -: cot(90-a) = cot(a)

and tan(90-a) = tan(a)

and cot(a) = 1/ tan(a)

so tan(a) ×cot(a) = tan(a)×1/tan(a) =1

so 3cot31° tan15° cot27° tan75° cot63° cot59°=

3cot31 × tan15× cot27 ×tan (90-15)×cot(90-17)×cot(90-31)=3cot31×tan31×tan15× cot15×cot27×tan27= 3×1×1×1 =3

Answer 2

Step-by-step explanation:

Given :-

3 cot31° tan15° cot27° tan75° cot63° cot59°

To find :-

Without using trigonometry tables, find the value of the expression ?

Solution :-

Given expression is

3 cot 31° tan 15° cot 27° tan 75° cot 63° cot 59°

=> 3(cot 31°cot 59°)(tan 15° tan 75°)(cot 27° cot 63°)

We know that

Tan (90°-A) = Cot A

Cot (90°-A) = Tan A

Cot 59° = Cot (90°-31°) = Tan 31°

Tan 75° = Tan (90°-15°) = Cot 15°

Cot 63° = Cot (90°-27°) = Tan 27°

=> 3(cot 31°tan 31°)(tan 15° cot 15°)(cot 27° tan 27°)

We know that

Tan A × Cot A = 1

=> 3(1)(1)(1)

=> 3

Answer:-

The value of the given expression is 3

Used Formulae :-

→ Tan (90°-A) = Cot A

→ Cot (90°-A) = Tan A

→ Tan A = 1/Cot A

→ Cot A = 1/Tan A

→ Tan A × Cot A = 1