If cos 43^{circ} + sin 43^{circ} = k, then fi | vedclass

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Question

(A) Given: $\cos 43^{\circ} + \sin 43^{\circ} = k$.Multiply both sides by $\frac{1}{\sqrt{2}}$:$\frac{1}{\sqrt{2}} \cos 43^{\circ} + \frac{1}{\sqrt{2}

Vedclass · Accepted Answer

$\frac{k}{\sqrt{2}}$

Vedclass · Answer

(A) Given: $\cos 43^{\circ} + \sin 43^{\circ} = k$.Multiply both sides by $\frac{1}{\sqrt{2}}$:$\frac{1}{\sqrt{2}} \cos 43^{\circ} + \frac{1}{\sqrt{2}} \sin 43^{\circ} = \frac{k}{\sqrt{2}}$.Using $\sin 45^{\circ} = \cos 45^{\circ} = \frac{1}{\sqrt{2}}$, we get:$\sin 45^{\circ} \cos 43^{\circ} + \cos 45^{\circ} \sin 43^{\circ} = \frac{k}{\sqrt{2}}$.Using the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$:$\sin(45^{\circ} + 43^{\circ}) = \frac{k}{\sqrt{2}}$.$\sin 88^{\circ} = \frac{k}{\sqrt{2}}$.Since $\sin 88^{\circ} = \cos(90^{\circ} - 88^{\circ}) = \cos 2^{\circ}$, we have:$\cos 2^{\circ} = \frac{k}{\sqrt{2}}$.

If $\cos 43^{\circ} + \sin 43^{\circ} = k$, then find the value of $\cos 2^{\circ}$.

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