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Grade: 11
        
Eliminate theta if tan(theta-alpha)=a and tan(theta+alpha)=b
29 days ago

Answers : (1)

Arun
15903 Points
							
We know that if -- 

Tan x = A 

=> x = Tan⁻¹ A 

Hence the given eqns can be re-written as -- 

.... θ - α = Tan⁻¹ a .................. (1) and also -- 
.... .θ + α = Tan⁻¹ b .................. (2) 
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ 
-- 2 α = Tan⁻¹ a - Tan⁻¹ b ...................... On subtraction 

=> Tan⁻¹ a - Tan⁻¹ b = -- 2 α
29 days ago
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