Question

please solve it...
I will mark as brainliest...!​

Answer 1

$\large{\underline{\underline{\mathfrak{\red{\sf{SOLUTION:-}}}}}}$.

$\large{\underline{\underline{\mathfrak{\sf{FIND\:HERE:-}}}}}$.

• Sin45° Cos30° + Cos30° Sin45°

Or,

• $\sin\:(45^{\circ}\:+\:30^{\circ})$

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$\large{\underline{\underline{\mathfrak{\red{\sf{EXPLANATION:-}}}}}}$.

$\bold{\underline{\:Using\:identity}}$

• $\sin\:(A+B)\:=\:(\sin A\cos B\:+\cos A\sin B)$

• $\sin\:(A-B)\:=\:(\sin A\cos B\:-\cos A\sin B)$

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Some Important Values

• $\sin45^{\circ}\:=\frac{1}{\sqrt{2}}$

• $\sin30^{\circ}\:=\frac{1}{2}$

• $\cos45^{\circ}\:=\frac{1}{\sqrt{2}}$

• $\cos30^{\circ}\:=\frac{\sqrt{3}}{2}$

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So ,

=> Sin(45°+30°) = Sin45° Cos30° + Cos30° Sin45°

Take L.H.S.,

=> Sin45° Cos30° + Cos30° Sin45°

Keep all values

$\implies\frac{1}{\sqrt{2}}\times\:\frac{\sqrt{3}}{2}\:+\:\frac{1}{\sqrt{2}}\times\:\frac{1}{2}$

$\implies\frac{\sqrt{3}}{2\sqrt{2}}\:+\frac{1}{2\sqrt{2}}$

$\implies\frac{(\sqrt{3}+1)}{2\sqrt{2}}$

So , we can say that

$\bold{\boxed{\boxed{\sin\:(45^{\circ}\:+\:30^{\circ})\:=\frac{(\sqrt{3}+1)}{2\sqrt{2}}}}}$

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Answer 2

$\large{\underline{\underline{\mathfrak{\red{\sf{SOLUTION:-}}}}}}$

.

$\large{\underline{\underline{\mathfrak{\sf{FIND\:HERE:-}}}}}$

.

Sin45° Cos30° + Cos30° Sin45°

Or,

\sin\:(45^{\circ}\:+\:30^{\circ})sin(45 ∘ +30 ∘ )

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$\large{\underline{\underline{\mathfrak{\red{\sf{EXPLANATION:-}}}}}}$

.

$\bold{\underline{\:Using\:identity}} </p><p>$

\sin\:(A+B)\:=\:(\sin A\cos B\:+\cos A\sin B)sin(A+B)=(sinAcosB+cosAsinB)

\sin\:(A-B)\:=\:(\sin A\cos B\:-\cos A\sin B)sin(A−B)=(sinAcosB−cosAsinB)

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Some Important Values

$\sin45^{\circ}\:=\frac{1}{\sqrt{2}}sin45$

$\sin30^{\circ}\:=\frac{1}{2}sin30$

$\cos45^{\circ}\:=\frac{1}{\sqrt{2}}cos45$

$\cos30^{\circ}\:=\frac{\sqrt{3}}{2}cos30$

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So ,

=> Sin(45°+30°) = Sin45° Cos30° + Cos30° Sin45°

Take L.H.S.,

=> Sin45° Cos30° + Cos30° Sin45°

Keep all values

$\implies\frac{1}{\sqrt{2}}\times\:\frac{\sqrt{3}}{2}\:+\:\frac{1}{\sqrt{2}}\times\:\frac{1}{2}⟹ 2$

$\implies\frac{\sqrt{3}}{2\sqrt{2}}\:+\frac{1}{2\sqrt{2}}⟹ </p><p>2$

$\implies\frac{(\sqrt{3}+1)}{2\sqrt{2}}⟹ </p><p>2$

So , we can say that

$\bold{\boxed{\boxed{\sin\:(45^{\circ}\:+\:30^{\circ})\:=\frac{(\sqrt{3}+1)}{2\sqrt{2}}}}} </p><p>sin(45$

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hope it helps uh ❤️!