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Question
(1 + tan θ)2 + (1 − tan θ)2 is equal to ______.
Options
2 coseс2 θ
2 sec2 θ
coseс2 θ
sec2 θ
MCQ
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Solution
(1 + tan θ)2 + (1 − tan θ)2 is equal to 2 sec2 θ.
Explanation:
Solving,
⇒ (1 + tan θ)2 + (1 - tan θ)2
⇒ 1 + tan2 θ + 2 tan θ + 1 + tan2 θ - 2 tan θ
⇒ 2 + 2 tan2 θ
⇒ 2(1 + tan2 θ)
Substituting, 1 + tan2 θ = sec2 θ, we get :
⇒ 2 sec2 θ.
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