Question

what is the biggest vaule of sin theata* cos theata​

Answer 1

Answer:

Step-by-step explanation:

f(θ)=sinθ+cosθ  

=2–√(12√sinθ+12√cosθ)  

=2–√(cosπ/4∗sinθ+sinπ/4∗cosθ)  

=2–√(sin(π/4+θ))  

As you know greatest

value of

sinθ=1  

so greatest value of

f(θ)=2–√∗1=2–√  

Another approach can be made by using calculus

f(θ)=sinθ+cosθ  

Differentiating w.r.t  θ  

f‘(θ)=cosθ−sinθ  

Equating it to zero we get ,

f‘(θ)= 0

cosθ−sinθ =0

cosθ=sinθ  

tanθ=1  

θ=π4  

So greatest value will be at θ=π4  [of course check that  f‘‘(θ)<0 ] i.e greatest value is  f(π4)  

=sinπ4+cosπ4  

=12√+12√  

=2–√