Given : Expression = sin² 60⁰ – sin 90⁰ Need To Evaluate : sin² 60⁰ – sin 90⁰ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ ❍ Trigonometric Ratios for standard angles : [tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}[/tex] ⠀⠀⠀⠀⠀By Seeing Table of Trigonometry Ratios for angles : [tex]\sin 60\degree = \dfrac {\sqrt{3}}{2}[/tex] [tex]\sin 90\degree = 1 [/tex] ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Expression = sin² 60⁰ – sin 90⁰ ⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex] [tex]\qquad :\implies \sf{ \sin^2 60\degree – \sin 90\degree}[/tex] [tex]\qquad :\implies \sf{ \bigg( \dfrac{\sqrt{3}}{2} \bigg)^2 – 1 }[/tex] [tex]\qquad :\implies \sf{ \dfrac{3}{4} – 1 }[/tex] [tex]\qquad :\implies \sf{ \dfrac{3-4}{4} }[/tex] [tex]\qquad :\implies \bf{Answer\:= \dfrac{-1}{4} }[/tex] ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Reply
Given : Expression = sin² 60⁰ – sin 90⁰
Need To Evaluate : sin² 60⁰ – sin 90⁰
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀
❍ Trigonometric Ratios for standard angles :
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}[/tex]
⠀⠀⠀⠀⠀By Seeing Table of Trigonometry Ratios for angles :
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Expression = sin² 60⁰ – sin 90⁰
⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]
[tex]\qquad :\implies \sf{ \sin^2 60\degree – \sin 90\degree}[/tex]
[tex]\qquad :\implies \sf{ \bigg( \dfrac{\sqrt{3}}{2} \bigg)^2 – 1 }[/tex]
[tex]\qquad :\implies \sf{ \dfrac{3}{4} – 1 }[/tex]
[tex]\qquad :\implies \sf{ \dfrac{3-4}{4} }[/tex]
[tex]\qquad :\implies \bf{Answer\:= \dfrac{-1}{4} }[/tex]
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Answer:
sin 2 60- sin 90
putting values of sin 60and 90
2*√3/2 – 1
√3- 1
thats the answer