cos theta. cosec theta – sin theta. sec theta / cosec theta + sin theta = codec theta. sec theta ​

Question

cos theta. cosec theta – sin theta. sec theta / cosec theta + sin theta = codec theta. sec theta ​

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Nevaeh 1 month 2021-08-18T07:52:08+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-18T07:53:16+00:00

    \underline\mathfrak\pink{To \: Proved:-}

    • \: \: \: \: \: \leadsto \: \: \frac{Cos \theta \: Cosec \theta \: - \: Sin \theta \: Sec \theta}{Cos \theta \: + \: Sin \theta} \: \: = \: \: Cosec \theta \: - \: Sec \theta

    \large\underline\mathfrak\pink{Solutions:-}

    LHS:-

    \: \: \: \: \: \leadsto \: \: \frac{Cos \theta \: Cosec \theta \: - \: Sin \theta \: Sec \theta}{Cos \theta \: + \: Sin \theta}

    \: \: \: \: \: \leadsto \: \: \frac{Cos \theta \: {(\frac{1}{Sin \theta})} \: - \: Sin \theta \: {(\frac{1}{Cos \theta})}}{Cos \theta \: + \: Sin \theta} \: \: \: \: \: \: {[Sec \theta \: \: = \: \: \frac{1}{Cos \theta} \: \: and \: \: Cosec \: \: = \: \:  \frac{1}{Sin \theta}]}

    \: \: \: \: \: \leadsto \: \: \frac{{(\frac{Cos \theta}{Sin \theta})} \: - \: {(\frac{Sin \: theta}{Cos \theta})}}{Cos \theta \: + \: Sin \theta}

    \: \: \: \: \: \leadsto \: \: \frac{\frac{{Cos}^{2} \theta \: - \: {Sin}^{2} \theta}{Sin \theta \: Cos \theta}}{Cos \theta \: + \: Sin \theta}

    \: \: \: \: \: \leadsto \: \: \frac{\frac{{({Cos} \theta \: - \: {Sin} \theta)} \: {({Cos} \theta \: + \: {Sin} \theta)}}{Sin \theta \: Cos \theta}}{Cos \theta \: + \: Sin \theta} \: \: \: \: \: {[{a}^{2} \: - \: {b}^{2} \: \: = \: \: {(a \: + \: b)} \: \: {(a \: - \: b)}]}

    \: \: \: \: \: \leadsto \: \: \frac{Cos \theta \: - \: Sin \theta}{Sin \theta \: Cos \theta}

    \: \: \: \: \: \leadsto \: \: \frac{Cos \theta}{Sin \theta \: Cos \theta} \: - \: \frac{Sin \theta}{Sin \theta \: Cos \theta}

    \: \: \: \: \: \leadsto \: \: \frac{1}{Sin \theta} \: - \: \frac{1}{Cos \theta}

    \: \: \: \: \: \leadsto \: \: Cosec \theta \: - \: Sec \theta

    \: \: \: \: \: \: \: RHS \: \: \leadsto \: \: Cosec \theta \: - \: Sec \theta

    • Proved
    0
    2021-08-18T07:53:49+00:00

    Answer:

    Hope it helps you…….

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