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प्रश्न
Which of the following is true?
विकल्प
sec2 θ + tan2 θ = 1
sec2 θ = tan2 θ − 1
sec2 θ = 1 + tan2 θ
tan2 θ = 2 − sec2 θ
MCQ
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उत्तर
sec2 θ = 1 + tan2 θ
Explanation:
sin2 θ + cos2 θ = 1
Divide every term by cos2 θ.
`sin^2 θ/cos^2 θ + cos^2 θ/cos^2 θ`
= `1/cos^2 θ`
Apply the Quotient and Reciprocal Identities:
`sin^2 θ/cos^2 θ = tan^2 θ`
`cos^2 θ/cos^2 θ = 1`
`1/cos^2 θ = sec^2 θ`
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