Prove that- cos 105-cos 15-sin 75-sin 15-

LHS: sin 75^∘ sin 15^∘ =cos(90^∘+15^∘)+cos(90^∘ 15^∘) = sin(15^∘ +sin75^∘ = sin75^∘ sin15^∘ ∴ cos105^∘+cos15^∘=sin75^∘ sin15^∘ Hence proved. ...

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Trigonometric Ratios of Compound Angles

Prove that: c...

Question

Prove that: $c o s 105^{\circ} + c o s 15^{\circ} = s i n 75^{\circ} - s i n 15^{\circ}$

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|\begin{matrix} \cos 15 ° & \sin 15 ° \\ \sin 75 ° & \cos 75 ° \end{matrix}|

∣ ∣ ∣ \begin{matrix} cos 15^{\circ} & sin 15^{\circ} sin 75^{\circ} & cos 75^{\circ} \end{matrix} ∣ ∣ ∣

\frac{\sin 15 ° \cos 75 ° + \cos 15 ° \sin 75 °}{\tan 5 ° \tan 30 ° \tan 35 ° \tan 55 ° \tan 85 °}

Evaluate $∣ ∣ ∣ \begin{matrix} c o s 15 & s i n 15 s i n 75 & c o s 75 \end{matrix} ∣ ∣ ∣$

(cos 75^{\circ} - cos 15^{\circ})^{2} + (sin 75^{\circ} - sin 15^{\circ})^{2}

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