Question

If sin a + cosec a = 2, show that sin^7 a + cosec^7 a = 2​

Answer 1

Answer:

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Answer 2

Answer:

Sin⁷a + Cosec⁷a = 2

Step-by-step explanation:

If sin a + cosec a = 2, show that sin^7 a + cosec^7 a = 2​

Sina + Coseca = 2

Coseca = 1/Sina

=> Sina + 1/Sina = 2

Multiplying by sina both sides

=> Sin²a + 1 = 2Sina

=> Sin²a - 2Sina + 1 = 0

=> (Sina - 1)² = 0

=> Sina - 1 = 0

=> Sina = 1

Cosec = 1/Sina = 1

LHS

= Sin⁷a + Cosec⁷a

= 1⁷ + 1⁷

= 1 + 1

= 2

= RHS