Simplify:
(sin θ + csc θ)2 + (cos θ + sec θ)2 - (tan θ - cot θ)2
Scroll down to see solution.
Answer:
(sin θ + csc θ)2 + (cos θ + sec θ)2 - (tan θ - cot θ)2 =
sin2θ + 2 sin θ csc θ + csc2θ + cos2θ + 2 cos θ sec θ + sec2θ - tan2θ + 2 tan θ cot θ - cot2θ =
sin2θ + 2 + csc2θ + cos2θ + 2 + sec2θ - tan2θ + 2 - cot2θ =
(sin2θ + cos2θ) + (csc2θ - cot2θ) + (sec2θ - tan2θ) + 6 =
1 + 1 + 1 + 6 =
9