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myrzilka [38]
3 years ago
5

Need Help !!

Mathematics
2 answers:
Ivanshal [37]3 years ago
6 0

Answer:

Given: sin θ – cos θ =0

Hence θ=45

Therefore

sin4 θ + cos4 θ.

sin4 45° + cos4 45°

2×(1/√2) ^4

2×1/4

Ans 1/2

Over [174]3 years ago
3 0

\huge \mathbb{\green{\fbox{\pink{ANSWER}}}}

\\  \:  \:  \implies \: sin^{4} \: \theta + cos^{4} \: \theta \rightarrow  \blue{ \frac{1}{2} }

\\ \\ \:  \large \mathfrak \green{Solution}  :

\\  \bf  \: Given :

\\ \sf \: \:  \bf sin \: \theta - cos \: \theta = 0

\\ \sf \rightarrow \: sin \:  \theta = cos \: \theta

\\ \sf \rightarrow \: \frac{sin \: \theta} {cos \: \theta} = 1

\\ \sf \rightarrow \: tan \: \theta = 1

\\ \sf \rightarrow \: tan \: \theta = tan \: 45 \degree

\\ \sf \rightarrow \: \theta = 45 \degree

\\ \\ \therefore \:  sin^{4} \: \theta + cos^{4} \: \theta

\\ \sf \rightarrow \: sin^{4} \: 45 \degree + cos^{4} \: 45 \degree

\\ \\\sf \rightarrow \: (\frac{1}{ \sqrt{2} } ) ^{4}  +(\frac{1}{ \sqrt{2} } ) ^{4}

\\ \sf \rightarrow \: ( \frac{1}{  \cancel {\sqrt{2} }}  )^{ \cancel{2}} ( \frac{1}{  \cancel{ \sqrt{2} }}  )^{\cancel{2}} + ( \frac{1}{  \cancel {\sqrt{2} }}  )^{ \cancel{2}} ( \frac{1}{  \cancel{ \sqrt{2} }}  )^{\cancel{2}}

\\ \\\sf \rightarrow \: \frac{1}{2} × \frac{1}{2} + \frac{1}{2}× \frac{1}{2}

\\ \\ \sf \rightarrow \: \frac{1}{4} +  \frac{1}{4}

\\ \\ \sf \rightarrow \: {\cancel \frac{2} {4}}

\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf  \implies \fbox{\pink {\frac{1}{2}}}

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