Trigonometric ratios of Angles Questions and solutions

Standard angles

$(1).\,\,$ Evaluate $\sin{45^\circ}\cos{45^\circ}\tan{45^\circ}$

$(2).\,\,$ Evaluate $\sin{60^\circ}\sin{30^\circ}$ $+$ $\cos{60^\circ}\cos{30^\circ}$

$(3).\,\,$ Evaluate $\dfrac{4}{\cot^2{30^\circ}}$ $+$ $\dfrac{1}{\sin^2{60^\circ}}$ $-$ $\cos^2{45^\circ}$

$(4).\,\,$ Evaluate $4(\sin^4{30^\circ}+\cos^4{60^\circ})$ $-$ $3(\cos^2{45^\circ}-\sin^2{90^\circ})$

Other angles

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