[tex]1-(cosx)^4[/tex] value is [tex]2sin^4-sin^4x[/tex] . Correct option is D) [tex]2sin^4-sin^4x[/tex] .
Step-by-step explanation:
Here we have , expression to evaluate:
[tex]1-(cosx)^4[/tex]
⇒ [tex]1-((cosx)^2)^2[/tex]
⇒ [tex]1-(1-(sinx)^2)^2[/tex]
We know that , [tex]sin^2x = 1-cos^2x[/tex] , putting value in equation [tex]1-(1-(sinx)^2)^2[/tex]
⇒ [tex]1-(1+sin^4x-2sin^4)[/tex]
⇒ [tex]1-1-sin^4x+2sin^4[/tex]
⇒ [tex]-sin^4x+2sin^4[/tex]
⇒ [tex]2sin^4-sin^4x[/tex]
Therefore , [tex]1-(cosx)^4[/tex] value is [tex]2sin^4-sin^4x[/tex] . Correct option is D) [tex]2sin^4-sin^4x[/tex]
