+1904 Prove the trignometric identity by first proving the left side is equal to the right side and then proving the right side is equal to the left side.
\(cot(\Theta )+tan(\Theta )=sec(\Theta )csc(\Theta )\)
+128475 cot θ + tan θ =
cos θ/ sin θ + sin θ/ cos θ get a common denominator of sin θ cos θ
[cos^2 θ + sin^2 θ] / [ sin θ cos θ]
1 / [ sin θ cos θ] =
[1/ sin θ] * [ 1 / cos θ ] =
csc θ sec θ = the RHS
To prove the other part, we can just reverse the steps above
sec θ csc θ =
1/cos θ * 1/ sin θ =
1/ [cos θ sin θ] =
[sin ^2 θ + cos ^2 θ] / cos θ sin θ] =
[sin^2 θ]/ [ sinθ cosθ] + [cos^2 θ]/ [ sin θ cos θ] =
sin θ / cos θ + cos θ / sin θ =
tan θ + cot θ = the LHS
+128475 cot θ + tan θ =
cos θ/ sin θ + sin θ/ cos θ get a common denominator of sin θ cos θ
[cos^2 θ + sin^2 θ] / [ sin θ cos θ]
1 / [ sin θ cos θ] =
[1/ sin θ] * [ 1 / cos θ ] =
csc θ sec θ = the RHS
To prove the other part, we can just reverse the steps above
sec θ csc θ =
1/cos θ * 1/ sin θ =
1/ [cos θ sin θ] =
[sin ^2 θ + cos ^2 θ] / cos θ sin θ] =
[sin^2 θ]/ [ sinθ cosθ] + [cos^2 θ]/ [ sin θ cos θ] =
sin θ / cos θ + cos θ / sin θ =
tan θ + cot θ = the LHS
