Question

( sec theta + tan theta) ( 1 - sin theta) = cos theta. Prove L. H. S. = R. H. S.​

Answer 1

Answer:

L.H.S= secΘ + tan Θ

R.H.S= cosΘ/ 1- sin Θ

taking R.H.S= cosΘ/ 1- sinΘ

multiplying numerator and denominator by (1+ sinΘ)

cosΘ (1+ sinΘ)/ (1- sinΘ) (1 + sinΘ)

cosΘ + cosΘsinΘ / 1 - sin^2Θ

cosΘ + cosΘsinΘ / cos^2 Θ

i.e. cosΘ/ cos^2 + cosΘsinΘ/ cos^2Θ

=> 1 / cosΘ + sinΘ / cosΘ

= secΘ = tan Θ = L.H.S

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

$\implies (sec\theta + tan\theta)(1-sin\theta)$

  We know, secθ = 1/cosθ

                   tanθ = sinθ/cosθ

              1 - sin^2 θ = cos^2 θ

Here,

$\implies \bigg( \dfrac{1}{cos\theta}+\dfrac{sin\theta}{cos\theta}\bigg)\bigg(1-sin\theta\bigg)\\\\\\\implies \dfrac{1}{cos\theta}\bigg( 1 + sin\theta\bigg)\bigg(1-sin\theta\bigg)\\\\\\\implies \dfrac{1}{cos\theta}( 1-sin^2 \theta)\\\\\\\implies \dfrac{1}{cos\theta}\times cos^2 \theta\\\\\\\implies cos\theta$

  Hence prpved