WyzAnt.comtrigonometry identity question
cos/sec x sin = csc - sin
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1 Answer
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]
