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sin21∘+sin22∘+sin23∘+…+sin288∘+sin289∘+sin290∘= ? \sin ^{ 2 }{ 1^{\circ} } +\sin ^{ 2 }{ 2^{\circ} } +\sin ^{ 2 }{ 3^{\circ} } + \ldots \\ +\sin ^{ 2 }{ 88^{\circ} } +\sin ^{ 2 }{ 89^{\circ} } +\sin ^{ 2 }{ 90^{\circ} } = \ ? sin21∘+sin22∘+sin23∘+…+sin288∘+sin289∘+sin290∘= ?
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sin2θ5=cos2θ6 \large \frac { \sin ^{ 2 }{ \theta } }{ 5 } =\frac { \cos ^{ 2 }{ \theta } }{ 6 }5sin2θ=6cos2θ
If θ\theta θ is a positive acute angle that satisfies the equation above, find sinθ\sin { \theta }sinθ.
Note: Give your answer to 3 decimal places.
∑k=150[(1+tan(k∘)+sec(k∘)) (1+cot(k∘)−csc(k∘))]= ? \displaystyle \sum_{k=1}^{50} \Bigg [ \bigg(1 + \tan(k^\circ)+\sec(k^\circ)\bigg)\ \bigg(1+\cot(k^\circ)-\csc(k^\circ) \bigg)\Bigg]=\ ? \ k=1∑50[(1+tan(k∘)+sec(k∘)) (1+cot(k∘)−csc(k∘))]= ?
(2+2)x+(2−2)x=2x \Large \left(\sqrt{2+\sqrt{2}}\right)^{x} + \left(\sqrt{2-\sqrt{2}}\right)^{x} = 2^{x}⎝⎛2+2⎠⎞x+⎝⎛2−2⎠⎞x=2x
Find the sum of all real xxx that satisfy the equation above.
1cos2θ+11+sin2θ+21+sin4θ+41+sin8θ \large\frac { 1 }{ \cos ^{ 2 }{ \theta } } +\frac { 1 }{ 1+\sin ^{ 2 }{ \theta } } +\frac { 2 }{ 1+\sin ^{ 4 }{ \theta } } +\frac { 4 }{ 1+\sin ^{ 8 }{ \theta } } cos2θ1+1+sin2θ1+1+sin4θ2+1+sin8θ4
If sin16θ=15 \large \sin ^{ 16 }{ \theta } = \frac { 1 }{ 5 } sin16θ=51, what is the value of the expression above?
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