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If sec(θ + α)/sec(θ – α) = a/b, then find the value of (cotθ.cotα).

If sec(θ + α)/sec(θ – α) = a/b, then find the value of (cotθ.cotα). Correct Answer (a + b)/(a – b)

GIVEN:

sec(θ + α)/sec(θ – α) = a/b

FORMULA USED:

cos (A + B) = cosA cosB – sinA sinB

cos (A – B) = cosA cosB + sinA sinB

CALCULATION:

sec(θ + α)/sec(θ - α) = a/b

⇒ cos(θ – α)/cos(θ + α) = a/b

⇒ (cosθ.cosα + sinθ.sinα)/(cosθ.cosα - sinθ.sinα) = a/b

Dividing numerator and denominator by Sinθ.Sinα

⇒ (cotθ.cotα + 1)/(cotθ.cotα - 1) = a/b

⇒ b × cotθ.cotα + b = a × cotθ.cotα – a

⇒ a × cotθ.cotα – b × cotθ.cotα = a + b

⇒ cotθ.cotα = (a + b)/(a – b)

∴ cotθ.cotα = (a + b)/(a – b)

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