Question

If sin theta minus cos theta equal to zero then find the value of sin power 4 theta + cos ki power 4 theta

Answer 1

Answer: $\dfrac{1}{2}$

Step-by-step explanation:

Given: $sin \theta - cos \theta = 0$

To find: $sin^4 \theta + cos^ 4 \theta$

As

$sin\theta - cos \theta = 0 \Rightarrow sin\theta = cos\theta \Rightarrow  tan \theta= 1 \therefore \theta = \dfrac{\pi}{4}$

Now

$sin^4 \theta + cos^ 4 \theta\\\\= sin^4\dfrac{\pi}{4} + cos^ 4 \dfrac{\pi}{4} \\\\= (\dfrac{1}{\sqrt{2} } )^4+(\dfrac{1}{\sqrt{2} } )^4= \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{1}{2}$

Hence, the value of $sin^4 \theta + cos^ 4 \theta$ is $\dfrac{1}{2}$

Answer 2

$Given \: sin \theta - cos \theta = 0$

$\implies sin\theta = cos\theta$

$\implies \frac{sin\theta}{cos\theta} = \frac{cos\theta}{cos\theta}$

$\implies tan \theta = 1$

$\implies tan \theta = tan \:45\degree$

$\implies \theta = 45\degree \: ---(1)$

$Now , the \: value \: of \: sin^{4}\theta - cos^{4}\theta \\= sin^{4} \:45\degree + cos^{4} \:45\degree \\= \left( \frac{1}{\sqrt{2}}\right)^{4} + \left( \frac{1}{\sqrt{2}}\right)^{4}\\= \frac{1}{4} + \frac{1}{4} \\= \frac{2}{4} \\= \frac{1}{2}$

Therefore.,

$\red {The \: value \: of \: sin^{4}\theta - cos^{4}\theta } \green {= \frac{1}{2}}$

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