Question

if sinA+cosecA=2 find sin^10A+cosec^10A

Answer 1

Given :- if sinA+cosecA=2 find sin^10A+cosec^10A

Solution :-

→ sin A + cosec A = 2

putting cosec A = (1/sin A)

→ sin A + (1/sin A) = 2

→ (sin²A + 1)/sin A = 2

→ sin²A + 1 = 2sin A

→ sin²A - 2sin A + 1 = 0

using a² - 2ab + b² = (a - b)²

→ (sin A - 1)² = 0

→ sin A - 1 = 0

→ sin A = 1

so,

→ cosec A = 1/sin A = 1 .

then,

→ sin¹⁰A + cosec¹⁰A

→ 1¹⁰ + 1¹⁰

→ 1 + 1

→ 2 (Ans.)

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