Search
Ask a question
0

cos/sec x sin = csc - sin

trigonometry identity question

1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Theresa C. | Dedicated, Patient Math TutorDedicated, Patient Math Tutor
4.9 4.9 (153 lesson ratings) (153)
1

Prove cos Θ/sec Θ sin Θ = csc Θ - sin Θ.

cos Θ/sec Θ sin Θ

=cos Θ / (1/cos Θ)(sin Θ)  note: [sec Θ = 1/cos Θ]

=cos2Θ/ sin Θ                   note:[cos Θ ÷ 1/cos Θ = cos Θ * cos Θ = cos2Θ]

=1 - sin2Θ/sin Θ                note:[cos2Θ = 1-sin2Θ]

=1/sin Θ - sin2Θ/sinΘ

=csc Θ - sin Θ                   note:[1/sin Θ = csc Θ]