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