Question

If sin θ − cos θ = 0 then the value of sin⁴θ + cos⁴θ

Options

• 1

• \[- 1\]

• \[\frac{1}{2}\]

• \[\frac{1}{4}\]

Answer 1

`bb(1/2)`

Explanation:

It is given that,

\[\sin\theta - \cos\theta = 0\]
\[ \Rightarrow \sin\theta = \cos\theta\]
\[ \Rightarrow \frac{\sin\theta}{\cos\theta} = 1\]
\[ \Rightarrow \tan\theta = 1\]
\[ \Rightarrow \tan\theta = \tan45°\]
\[ \Rightarrow \theta = 45°\] 

\[\therefore \sin^4 \theta + \cos^4 \theta\]

\[ = \sin^4 45° + \cos^4 45°\]

\[ = \left( \frac{1}{\sqrt{2}} \right)^4 + \left( \frac{1}{\sqrt{2}} \right)^4 \]

\[ = \frac{1}{4} + \frac{1}{4}\]

\[ = \frac{1}{2}\]