Question

Prove that ( sec A + tan A )(1-sin A )= cos A​

Answer 1

$\huge{\orange{\underline{\underline{\bf{AnSweR:}}}}}$

Given,

☞ (secA+tanA)(1−sinA)

$→\;{\bf{(\frac{1}{cos\;A}+\frac{sin\;A}{cos\;A})(1-sin\;A)}}$

$→\;{\bf{(\frac{1+sin\;A}{cos\;A})(1-sin\;A)}}$

$→\;{\bf{\frac{(1-sin\;A)(1-sin\;A)}{cos\;A}}}$

$→\;{\bf{\frac{(1-sin\;A)²}{cos\;A}}}$

$→\;{\bf{\frac{(1-sin²A)}{cos\;A}}}$

$→\;{\sf{\frac{cos²\;A}{cos\;A} = cos\;A}}$

Hence, Proved that

$\red{\bf{∴(secA+tanA)(1−sinA)=cosA}}$

Answer 2

Answer:

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