Question:

 Let tan⁡α=aa+1 and tan⁡β=12a+1 then α+β is 

Updated On: Feb 15, 2024
  • (A) π/4
  • (B) π/3
  • (C) π/2
  • (D) π
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The Correct Option is A

Solution and Explanation

Explanation:
tan⁡α=aa+1,tan⁡β=12a+1tan⁡(α+β)=aa+1+12a+11−a(a+1)(2a+1)=a(2a+1)+a+1(a+1)(2a+1)(a+1)(2a+1)−a(a+1)(2a+1)=2a2+2a+12a2+2a+1=1α+β=π4
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