Question

Tan22+tan23+tan22+tan23=1 prove that

Answer 1

Hi,
Here is the answer to your query:-

▶Formula used:(from trigonometry)
✅Tan(A+B)=(tanA+tanB)/(1-tanA*tanB)

Let A=22°,B=23°

Tan(22°+23°)=(tan22°+tan23°)/(1-tan22°×tan23°)

From trigonometry, we know tan45°=1

Therefore tan(45°)=1=(tan22°+tan23°)/(1-tan22°tan23°)

=> 1-tan22°tan23°=tan22°+tan23°

=> tan22°+tan23°+tan23°tan22° =1

Hence proved.

✅Thanks
@SHIVAM

Answer 2

tan22+cot(90-68)+tan23+cot(90-67)=1

tan22+cot22+tan23+cot230=1

tan22+1/tan22+tan23+1/tan23 =1

1 = 1