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Question

If tan (π4+θ)+tan(π4θ)=λ sec 2θ, then


A

3

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B

4

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C

1

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D

2

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Solution

The correct option is D

2


Given:

tan(π4+θ)+tan (π4θ)=λ sec 2θ tan π4+tan θ1tan π4×tan θ+tan π4tan θ1+tan π4×tan θ=λ sec 2 θ 1+tan θ1tan θ+1tan θ1+tan θ=λ sec 2θ (1+tan θ)2(1tan θ)2(1tan θ)+(1+tan θ)=λ sec 2θ

2(1+tan2 θ)1tan2 θ=λ sec 2θ 2 sec2θ1tan2θ=λ sec 2θ 2cos2 θ(1tan2θ)=λ sec 2θ 2cos2 θ(1sin2 θcos2 θ)=λ sec 2θ 2cos2 θsin2 θ=λ sec 2θ

2cos 2θ=λ sec 2θ 2 sec 2θ=λ sec 2θ 2=λ λ=2


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