Question

If sin+ cosec=2, then the value of sin-7 + cosec7 is

Answer 1

Answer:

2

Step-by-step explanation:

I think question is like this

If Sinθ + Cosecθ = 2 then find the value

of ( Sin⁷θ + Cosec⁷θ ) .

Solution ---> ATQ

Sinθ + Cosecθ = 2

We know that , Cosecθ = 1 / Sinθ

=> Sinθ + 1 / Sinθ = 2

Taking Sinθ as LCM we get

=> (Sin²θ + 1) / Sinθ = 2

=> Sin²θ + 1 = 2 Sinθ

=> Sin²θ - 2 Sinθ + 1 = 0

=> ( Sinθ )² - 2 ( Sinθ ) ( 1 ) + ( 1)² = 0

We have an identity

a² + b² - 2ab = ( a - b )² , using it here we get

=> ( Sinθ - 1 )² = 0

Taking square root of both sides we get

=> Sinθ - 1 = 0

=> Sinθ = 1

We know that

Cosecθ = 1 / Sinθ

= 1 / 1 = 1

Now we have to find value of

Sin⁷θ + Cosec⁷θ = ( Sinθ )⁷ + ( Cosecθ )⁷

= ( 1 )⁷ + ( 1 )⁷

We know that ( 1 )ⁿ = 1 , use it here

= 1 + 1

= 2