Question

(sec A+tan A) (1-sin A) =cos A​

Answer 1

Answer:

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Answer 2

Answer:

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Explanation:Answer:

$Given \ that \ (secA+ tanA)(1-sinA)=cosA\\\\We \ have \ to \ prove \ it\\\\L.H.S.=(secA+ tanA)(1-sinA)\\\\L.H.S=secA-secA.sinA+tanA-tanA.sinA \ ( just \ only \ multiplied \ it.)\\\\L.H.S=\frac{1}{cosA}-\frac{1}{cosA}\times sinA+tanA-tanA.sinA \ (put \ sec=\frac{1}{cosA})\\\\L.H.S=\frac{1}{cosA}-\frac{sinA}{cosA}+tanA-tanA.sinA\\\\We \ know \ that \ tanA=\frac{sinA}{cosA}\\\\L.H.S=\frac{1}{cosA}-tanA+tanA-sinA \times\frac{sinA}{cosA} \\\\L.H.S=\frac{1}{cosA}-\frac{sin^{2}A}{cosA}$

$L.H.S.=\frac{1-sin^{2}}{cosA}\\\\We \ know \ that \ 1-sin^{2}=cos^{2}A\\\\L.H.S=\frac{cosA \times cosA}{cosA}\\\\L.H.S=cosA\\\\Since \ L.H.S.=R.H.S\\\\PROVED$

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