Question

find value of (1-cot 23)(1-cot22)

Answer 1

Answer:

Step-by-step explanation:

Using cot(a+b) = (cota cotb -1) / (cota + cotb)

cot(22° + 23°) = cot45°

⇒ (cot22° cot23° - 1) / (cot22° + cot23°) = 1      (cot45° = 1)

⇒ cot22° cot23° - 1 = cot22° + cot23°

⇒ cot22° cot23° - cot22° - cot23 = 1

⇒ cot22° cot23° - cot22° - cot23° + 1 = 2  (add 1 to both sides)

⇒ - cot22° (1 - cot23°) +1 (1 - cot23°) = 2

⇒ (1 - cot23°)(1 - cot22°) = 2

Answer 2

The value of (1-cot 23°)(1-cot 22°) is 2.

Given :

The expression (1-cot 23) (1-cot 22)

To find :

The value of the given expression

Solution :

Let (1-cot 23) (1-cot 22) = √ k

L.H.S

= { (sin 23° - cos 23°) ( sin 22° - cos 22°) } / sin 23° sin 22°

Multiplying and dividing by √2, we can apply the formula of sin(A−B)

=> (sin 23° - cos 23°) = √2 ( cos 45° sin 23° - sin 45° cos 23° )

Similarly, sin 22° - cos 22° = √2 ( cos 45° sin 22° - sin 45° cos 22° )

= √2 ( sin (23° - 45°) . √2 ( sin ( 22° - 45°) ) / sin 23° sin 22°

= √4

= √(2 × 2)

= 2

Hence, the value of (1-cot 23°)(1-cot 22°) is 2.

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