Question

if sin A + cosec A =2.then , the value of sin^8A + cosec^8A =
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

As we know CosecA=1/SinA,

let SinA=x, So CosecA=1/x,

Now we know that, by identity

if x+1/x=a,then x^2+1/x^2=a^2-2

now by applying this identity we will get

x^2+1/x^2=2;

now again applying the identity we will get

x^4+1/x^4=2;

now again applying the identity we will get

x^8+1/x^8=2;

so the Answer of sin^8A + cosec^8A=2

Or Alternate Method

sinA+cosecA=2

sinA+1/sinA=2

sin^2A+1=2sinA

sin^2A-2sinA+1=0

(sinA-1)^2=0

sinA-1=0

sinA=1

cosecA= 1/sinA= 1/1 = 1.

Now sin^8A+cosec^8A

= (1)^8 + (1)^8

= 1 + 1

=2 Answer