Use identities to express each of the following in terms of sin Ө and cos Ө. Simplify your answers.?
21. sec^2 Ө - tan^2 Ө
22. tan^2 Ө (1 + cot^2 Ө)
23. csc Ө + cot Ө
24. csc^2 Ө + sec^2 Ө
25. tan Ө - sec Ө csc Ө
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21.
sec^2 Ө - tan^2 Ө
=1/cos^2 Ө - sin^2 Ө/cos^2 Ө
=(1-sin^2 Ө)/cos^2 Ө
= cos^2 Ө/cos^2 Ө =1
22.
tan^2 Ө (1 + cot^2 Ө)
=sin^2Ө/cos^2 (1+cos^2Ө/sin^2Ө)
=sec^2Ө
23.
csc Ө + cot Ө
= (1+cosӨ)/sinӨ
24.
csc^2 Ө + sec^2 Ө
=csc^2Өsec^2Ө
25.
tan Ө - sec Ө csc Ө
=(sin^2Ө -1)/sinӨcosӨ
=-cos^2Ө/sinӨcosӨ
=-cotӨ