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Grade 88 grade maths

Pls correct me
Find max value of sin^113@.cos^113@
=> (1/2 )^113(2sin@cos@)^113
=>(1/2)^113 (sin2@)^113
Here I know that the max value of sin@=sin^2@=1
But I am getting the angle as 2@. How to go with this?
Thank you.

Profile image of Seema
10 Years agoGrade 8
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1 Answer

Profile image of Arnav Prasad
ApprovedApproved Tutor Answer10 Years ago
Cos113@.Sin113@ = (Cos@.Sin@)113
(Cos@.Sin@)113 = ((Sin2@)/2)113
 
NOTE :
Maximum value of Sin2@ is same as that of Sin@.
That is, 1.
Proof? Let 2@ be ANY other angle. (Say X)
Maximum of Sin(Any thing inside the function) = 1.
 
(Sin2@)/2 = ½ = 2-1
Therefore,
((Sin2@)/2)113 maximum value is equal to (2-1)113.
 
The final answer is 2-113.

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