What is (tan x + tan y)(1 – cot x cot y) + (cot x + cot y)(1 – tan x tan y) equal to?
What is (tan x + tan y)(1 – cot x cot y) + (cot x + cot y)(1 – tan x tan y) equal to? Correct Answer 0
Given:
(tan x + tan y)(1 – cot x cot y) + (cot x + cot y)(1 – tan x tan y)
Formula Used:
tan 45° = cot 45° = 1
Calculation:
(tan x + tan y)(1 – cot x cot y) + (cot x + cot y)(1 – tan x tan y)
We can easily solve it by value putting:
Put x = y = 45°
⇒ (1 + 1)(1 – 1 × 1) + (1 + 1)(1 – 1 × 1)
⇒ 0 + 0
⇒ 0
∴ The value of (tan x + tan y)(1 – cot x cot y) + (cot x + cot y)(1 – tan x tan y) is 0.
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Feb 20, 2025