Question

please answer it and solve it on the paper​

Answer 1

Answer:

18

Step-by-step explanation:

$\sf \bf :\longmapsto sin^25^0 + sin^210^0 + sin^215^0 + .. .. sin^2180^0$

$\sf \bf :\longmapsto cos^2(90^0 - 85^0) + cos^2(90^0 - 80^0) + .. .. sin^245^0.. .. + sin^285^0.. .. + sin^2180^0$

$\sf \bf :\longmapsto cos^285^0+ cos^210^0 + cos^275^0 .. .. sin^245^0 .. .. + sin^285^0+ sin^290^0.. .. sin^2180^0$

$\sf \bf :\longmapsto 1 + 1 + 1 .. .. + \dfrac{1}{2} + .. .. + 1 + .. .. sin^2180^0$

$\sf \bf :\longmapsto 8 + \dfrac{1}{2} + 1 + sin^2(180^0- 85^0) + sin^2(180^0-80^0) + .. .. sin^2(180^0-5^0) + 0$

$\sf \bf :\longmapsto \dfrac{19}{2} + sin^285^0 + sin^280^0+ .. .. sin^25^0$

$\sf \bf :\longmapsto \dfrac{19}{2} + 8 + \dfrac{1}{2}$

$\sf \bf :\longmapsto 18$

Concepts used:

$\sf \bf cos(90^0 - A) = sinA$

$\sf \bf sin^2A + cos^2A = 1$

$\sf \bf sin(180^0 - A) = sinA$

Additional information:

$\sf \color{aqua}{Trigonometry\: Table}\\ \purple{\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \sf \red{\angle A} & \red{\sf{0}^{ \circ} }&\red{ \sf{30}^{ \circ} }& \red{\sf{45}^{ \circ} }& \red{\sf{60}^{ \circ}} &\red{ \sf{90}^{ \circ}} \\ \hline \\ \rm \red{sin A} & \green{0} & \green{\dfrac{1}{2}}& \green{\dfrac{1}{ \sqrt{2} }} &\green{ \dfrac{ \sqrt{3}}{2} }&\green{1} \\ \hline \\ \rm \red{cos \: A} & \green{1} &\green{ \dfrac{ \sqrt{3} }{2}}&\green{ \dfrac{1}{ \sqrt{2} }} & \green{\dfrac{1}{2}} &\green{0} \\ \hline \\\rm \red{tan A}& \green{0} &\green{ \dfrac{1}{ \sqrt{3} }}&\green{1} & \green{\sqrt{3}} & \rm \green{\infty} \\ \hline \\ \rm \red{cosec A }& \rm \green{\infty} & \green{2}& \green{\sqrt{2} }&\green{ \dfrac{2}{ \sqrt{3} }}&\green{1} \\ \hline\\ \rm \red{sec A} & \green{1 }&\green{ \dfrac{2}{ \sqrt{3} }}& \green{\sqrt{2}} & \green{2} & \rm \green{\infty} \\ \hline \\ \rm \red{cot A }& \rm \green{\infty} & \green{\sqrt{3}}& \green{1} & \green{\dfrac{1}{ \sqrt{3} }} & \green{0}\end{array}}}}$

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