Question

If sin theta minus cos theta is equal to zero then the value of sin 4 theta + cos 4 theta is

Answer 1

From the above equation, we get

cosθ=sinθ

Hence

θ=45°

Therefore

$\bold{sin^4 θ+cos^4θ}$

$\bold{=sin^4 45°+cos^4 45°}$

$= 2 \times ( \frac{1}{ \sqrt{2} } ) {}^{4}$

$= 2 \times \frac{1}{4}$

$= \frac{1}{2}$