Question

cosa/1-sina +1- sin a/cosa = 2 seca​

Answer 1

Answer:

$\huge\mathcal{\green{Hola!}}$

$\huge\mathfrak{\red{Answer}}$

Step-by-step explanation:

☆ To prove:-

$\huge \frac{ \: cos \: A}{1 - sin \: A} - \frac{1 - sin \: A}{cos \: A} = 2 \: sec \: A$

☆ Trigonometric identities:-

${sin}^{2} A \: + {cos}^{2} A = 1$

${sec}^{2} A - {tan}^{2} A = 1$

${cosec}^{2} A = 1 + {cot}^{2} A$

☆ Required Solution:-

: ➝ LHS:-

• Taking the LCM we have;

$\frac{ {cos}^{2}A + {(1 - sin \: A})^{2} }{cos \: A(1 - sin \: A)}$

• Using the identity (a-b)^2 = a^2 + b^2 - 2ab we have;

$= \frac{ {cos}^{2}A + 1 + {sin}^{2}A - 2sin \: A }{cos \: A(1 - sin \: A)}$

• As cos^2 A + sin^2 A = 1

$\huge\mathcal{\green{Therefore,}}$

$= > \frac{1 + 1 - 2 \: sin \: A}{cos \: A(1 - sin \: )} = \frac{2 - 2sin \: A}{cos \: A(1 - sin \: A)}$

$\frac{2(1 - sin \: A)}{cos \: A(1 - sin \: A)} = \frac{2}{cos \: A} = 2 \: sec \: A$

= RHS

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Answer 2

Answer:

nice misstriquil your answer is correct

Step-by-step explanation:

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