Question

$\sf\tiny{\purple{If \: sin \: θ \: - \: cos \: θ \: = \: 0, \: then \: the \: value \: of \: (sin^4θ - cos^4θ) = ?}}$​

Answer 1

Answer:

Given :-

Sin θ- cosθ= 0, then value of (sin⁴θ-cos⁴θ) ?

Solutions :-

$sinθ - cosθ = 0$

$sinθ = cosθ$

$\frac{sinθ}{cosθ} = 1$

$tanθ = 1$

$θ = \frac{\pi}{4}$

Now,

$sin {}^{4} θ + cos {}^{4} θ = (sin \frac{\pi}{4} ) {}^{4} +(cos \frac{\pi}{4} ) {}^{4} =$

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

So,

$sin {}^{4} θ + cos {}^{4} θ = \frac{1}{2}$

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Answer 2

Answer:

From the above equation, we get

cosθ=sinθ

Hence

θ=450

Therefore

sin 4 θ+cos 4θ

=sin 4 45 0 +cos 4450

Step-by-step explanation:

hence the correct answer is 1/2