Question

3. The maximum value of
sin 2020(x) + cos2020(x) is​

Answer 1

y=sinx−cosx,

dx

dy

​

=cosx+sinx

dx

2

d

2

y

​

=−sinx+cosx=−(sinx−cosx)

=−y. (negative) hence a maxima.

Further for maxima

dx

dy

​

=0

⇒cosx+sinx=0

⇒tanx=−1=tan

4

3π

​

∴x=

4

3π

​

∴ Maximum value of (\sin x - \cos x)

=sin

4

3π

​

−cos

4

3π

​

=(

2

​

1

​

)−(−

2

​

1

​

)=

2

​

1

​

+

2

​

1​ = 2 2 =