Question

What is the value of sin³45⁰+cos³45⁰?​

Answer 1

Answer:

The answer is $\dfrac{1}{\sqrt 2}$

Step-by-step explanation:

Concept :

            $\sin45^\circ=\dfrac{1}{\sqrt 2}$ and $\cos45^\circ=\dfrac{1}{\sqrt 2}$

Therefore   $\sin^345^\circ+\cos^345^\circ$

                  $=(\dfrac{1}{\sqrt 2})^3+(\dfrac{1}{\sqrt 2})^3\\=2(\dfrac{1}{\sqrt 2})^3=2(\dfrac{1}{\sqrt 2})^2(\dfrac{1}{\sqrt 2})\\=2(\dfrac{1}{2}(\dfrac{1}{\sqrt 2}))=\dfrac{1}{\sqrt 2}$