Mathematics
Assertion (A): If sec θ + tan θ = a and sec θ − tan θ = b then ab = 1.
Reason (R): sec2 θ - tan2 θ = 1
(A) is true and (R) is false.
(A) is false and (R) is true.
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both (A) and (R) are true, but (R) is not the correct explanation of (A).
Trigonometric Identities
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Answer
Given,
⇒ sec θ + tan θ = a
⇒ sec θ − tan θ = b
⇒ ab = (sec θ + tan θ)(sec θ - tan θ)
⇒ ab = sec2 θ - tan2 θ
⇒ ab = 1
So assertion (A) is true.
We know that,
⇒ sec2 θ - tan2 θ = 1
This is a fundamental trigonometric identity.
Thus, Both (A) and (R) are true and (R) is the correct explanation of (A).
Hence, option 3 is the correct option.
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