Question

If x = a(Cosec A + Cot A) and y = b(1 - Cos A/Sin A) then find the value of xy.​

Answer 1

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Answer 2

ANSWER:

The value of xy = ab.

GIVEN:

x = a(Cosec A + Cot A)

y = b(1 - Cos A)/Sin A

TO FIND:

The value of xy.

FORMUALE:

★ 1 / Sin A = Cosec A

★ Cos A / Sin A = Cot A

★ Cosec² A - Cot² A = 1

★ (A + B)(A - B) = A² - B²

EXPLANATION:

xy = a(Cosec A + Cot A) × b(1 - Cos A)/SinA

(1 - Cos A)/SinA = 1/Sin A - Cos A/Sin A

(1 - Cos A)/SinA = Cosec A - Cot A

Substitute (1 - Cos A)/SinA = Cosec A - Cot A in xy = a(Cosec A + Cot A) × b(1 - Cos A)/SinA

xy = a(Cosec A + Cot A) × b(Cosec A - Cot A)

xy = ab(Cosec² A - Cot² A)

xy = ab(1)

xy = ab

The value of xy = ab.