Question

express the ratios cosA tan A and sec A in terms of sin A ​

Answer 1

Answer:

Step-by-step explanation:

Heya!!!

cos A

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sin^2 A + cos^2 A= 1

cos^2 A = 1 - sin^2 A

cos A = root of (1-sin^2 A)

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tan A

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tan A = sin A / cos A

=sinA / root of ( 1- sin^2 A)

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sec A

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sec A = 1 / cos A

=1/ root of (1-sin^2 A)

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HOPE IT HELPS

pls mark brainliest

Answer 2

SINCE,

$\large\sf{{cos}^{2} A + {sin}^{2} A = 1,}$

THEREFORE, ,

$\large\sf{{cos}^{2} A = 1 - {sin}^{2} A}$

i.e., $\large\sf{cos \: a = + \sqrt{1 - {sin}^{2} a}}$

$\huge\sf\purple{cos\:A=√1-{sin}^{2}A}$

HENCE,

$\large\sf{tan\:A=\frac{sin\:A}{cos\:A}=\frac{sin\:A}{√1-{sin}^{2}A}}$

AND

$\large\sf{sec\:A=\frac{1}{cos\:A}=\frac{1}{√1-{sin}^{2}A}}$