1(v)
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)(A) is true and (R) is false.
- (b)(A) is false and (R) is true.
- (c)Both (A) and (R) are true and (R) is the correct explanation of (A).
- (d)Both (A) and (R) are true, but (R) is not the correct explanation of (A).
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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.