value of: $$ \frac{\sin heta+\cos heta}{2 \sin heta} $$ without using a calculator. $$ 4.2 .1 an \left(-32^{\circ} ight) $$ $$ 4.2 .2 \sin 412^{\circ} $$ Simplify the following fully and without using a calculator: $$ \frac{\sin 120^{\circ} \cdot an 300^{\circ}}{\cos \left(-60^{\circ} ight) \cdot an 225^{\circ}} $$ Prove the following identity: $$ \frac{\cos 2 x-\cos x-\sin x}{2 \sin x \cos x+\sin x}=\frac{1}{ an x}-\frac{1}{\sin x} $$ Determine the general solution of: $$ \sin (5 heta)=\cos \left( heta-40^{\circ} ight) $$

Question

value of: $$ \frac{\sin 	heta+\cos 	heta}{2 \sin 	heta} $$ without using a calculator. $$ 4.2 .1 	an \left(-32^{\circ}ight) $$ $$ 4.2 .2 \sin 412^{\circ} $$ Simplify the following fully and without using a calculator: $$ \frac{\sin 120^{\circ} \cdot 	an 300^{\circ}}{\cos \left(-60^{\circ}ight) \cdot 	an 225^{\circ}} $$ Prove the following identity: $$ \frac{\cos 2 x-\cos x-\sin x}{2 \sin x \cos x+\sin x}=\frac{1}{	an x}-\frac{1}{\sin x} $$ Determine the general solution of: $$ \sin (5 	heta)=\cos \left(	heta-40^{\circ}ight) $$

Pope Chavez · Accepted Answer

1. $$ \frac{1}{2} + \frac{1}{2} \cot 	heta $$ 2. $$ -4.2 	an(32^{\circ}) $$ 3. $$ 8.4 \sin 52^{\circ} $$ 4. $$ -3 $$ 5. The identity is proven.

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