Question

sinx + cosecx = 2 then sin^4x + cosec^4 x=?

Answer 1

hey your ans is here


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given:-

sin x + cosec x= 2

to find:-

sin 4 x + cosec 4 x= ?


now apply identity = (a+b)2=a2+b2+2ab

so

(sin x+cosecx)2=sin2x+cosec2x+2×sinx×cosecx=(2)^2

so


sin2x+cosec2x+2×sinx×1/sin x=4
sin2x+cosec2x=4-2=2

now we got
sin 2 x+ cosec 2 x =2

again apply identity

(a2+b2)^2=a4+b4+4ab

so

(sin2x+cosec2x)^2=sin 4 x + cosec 4 x+4
(2)^2=sin 4 x + cosec 4 x +4

0=sin 4 x+ cosec 4 x

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important points:-
cosec=1/sin

sin =1/cosec


which we applied in identity

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Answer 2

=sin^4x+cosec^4x

={sin^2x+cosec^2x}^2-2sin^2xcosec^2x

=[{sinx+cosecx}^2-2sinxcosecx]^2-2sin^2x×1/sin^2x

=[{2}^2-2×sinx×1/sinx]^2-2

=[4-2]^2-2

=[2]^2-2

=4-2

=2

SO sin^4x+cosec^4x=2 i will hope that this answer is ryt