document.write( "Question 986288: If tan theta=cot<60`+theta> find the value of theta\r
\n" ); document.write( "\n" ); document.write( "tanΘ = cot(60 + Θ) , Find the value of Θ \n" ); document.write( "
Algebra.Com's Answer #607078 by sanusi hammed (1)\"\" \"About 
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If tan theta=cot<60`+theta> find the value of theta\r
\n" ); document.write( "\n" ); document.write( " SOLUTION\r
\n" ); document.write( "\n" ); document.write( "tanΘ = cot(60 + Θ) , Find the value of Θ\r
\n" ); document.write( "\n" ); document.write( "Note: tanΘ = sinΘ/cosΘ
\n" ); document.write( "And Also Note: cotΘ = cosΘ/sinΘ\r
\n" ); document.write( "\n" ); document.write( "Hence, tanΘ = cot(60 + Θ)\r
\n" ); document.write( "\n" ); document.write( "∴(sinΘ/cosΘ) = [cos(60 + Θ)/sin(60 + Θ)]\r
\n" ); document.write( "\n" ); document.write( " By equating numerator with numerator and denominator with denominator, we get. .\r
\n" ); document.write( "\n" ); document.write( " ∴ sinΘ = cos(60 + Θ) \r
\n" ); document.write( "\n" ); document.write( "From trigonometry identity:sinΘ = cos(90 - Θ)\r
\n" ); document.write( "\n" ); document.write( "By comparing the equation, we got. ..\r
\n" ); document.write( "\n" ); document.write( " cos(60 + Θ) = cos(90 - Θ)\r
\n" ); document.write( "\n" ); document.write( " Council out cos, we will get \r
\n" ); document.write( "\n" ); document.write( " ∴ 60 + Θ = 90 - Θ\r
\n" ); document.write( "\n" ); document.write( " Collect the like term\r
\n" ); document.write( "\n" ); document.write( " ∴ Θ + Θ = 90 - 60\r
\n" ); document.write( "\n" ); document.write( " ∴ 2Θ = 30\r
\n" ); document.write( "\n" ); document.write( " Divide both side by 2\r
\n" ); document.write( "\n" ); document.write( " ∴ Θ = 30/2\r
\n" ); document.write( "\n" ); document.write( " ∴ Θ = 15 °\r
\n" ); document.write( "\n" ); document.write( "By equating the denominator, we will have\r
\n" ); document.write( "\n" ); document.write( " CosΘ = sin(60 + Θ)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From trigonometry identity: cosΘ = sin(90 - Θ)\r
\n" ); document.write( "\n" ); document.write( " By comparing the equation, we get\r
\n" ); document.write( "\n" ); document.write( " sin(60 + Θ) = sin(90 - Θ)\r
\n" ); document.write( "\n" ); document.write( " Cos will council out, we get\r
\n" ); document.write( "\n" ); document.write( " 60 + Θ = 90 - Θ\r
\n" ); document.write( "\n" ); document.write( " Collect the like term\r
\n" ); document.write( "\n" ); document.write( " ∴ Θ + Θ = 90 - 60\r
\n" ); document.write( "\n" ); document.write( " ∴ 2Θ = 30\r
\n" ); document.write( "\n" ); document.write( " Divide both side by 2\r
\n" ); document.write( "\n" ); document.write( " ∴ Θ = 30/2\r
\n" ); document.write( "\n" ); document.write( " ∴ Θ = 15 °\r
\n" ); document.write( "\n" ); document.write( "Therefore the value of theta , Θ = 15°\r
\n" ); document.write( "\n" ); document.write( "Checking:\r
\n" ); document.write( "\n" ); document.write( "tanΘ = cot(60 + Θ)\r
\n" ); document.write( "\n" ); document.write( "tan15° = cot(60 + 15°)\r
\n" ); document.write( "\n" ); document.write( "tan15° = cot75°\r
\n" ); document.write( "\n" ); document.write( "Note: cotΘ = 1/tanΘ\r
\n" ); document.write( "\n" ); document.write( "tan15° = 1/tan75°\r
\n" ); document.write( "\n" ); document.write( "0.267949192 = 1/(3.732050808)\r
\n" ); document.write( "\n" ); document.write( "0.267949192 = 0.267949192\r
\n" ); document.write( "\n" ); document.write( "Therefore, the value of theta , Θ = 15°\r
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