Question

prove that if sina + cosa =2 then prove that sin⁴A+cosec⁴A =2


PLS I NEED THE ANSWER QUICKLY . FIRST ONE TO ANSWER WILL BE MARKED BRAINLIEST ​

Answer 1

it seems that the question has a flaw

instead of

sin a + cos a = 2

it should be

sin a + cosec a = 2

I am proceeding to solve taking this as correct

sin a + cosec a = 2

squaring both side

(sin a + cosec a )^2 = 2^2

sin^2 a + cosec^2 a + 2 sin a cosec a = 4

sin^2 a + cosec ^2 a + 2 sin a * 1/ sin a = 4

sin^2 a + cosec ^2 a + 2 = 4

sin^2 a + cosec ^2 a = 4 - 2

sin^2 a + cosec ^2 a = 2

again squaring both side

(sin^2 a + cosec^2 a )^2 = 2^2

(sin^2 a)^2 + (cosec^2 a)^2 + 2 sin^2 a cosec^2 a = 2^2

sin^4 a + cosec^4 a + 2 = 4

sin^4 a + cosec^4 a = 4 - 2

sin^4 a + cosec ^2 a = 2

proved