Question

secA(1-sinA)(secA+tanA)​

Answer 1

hope this answer will be helpful ♥️♥️

Answer 2

Question :

secx(1-sinx)(secx+tanx)

Trignometric Formula's:

$1) \sin {}^{2} (x) + \cos {}^{2} (x) = 1$

$2)1 + \tan {}^{2} (x) = \sec {}^{2} (x)$

$3)1 + \ \cot{}^{2} (x) = \ \csc {}^{2} (x)$

$4) \sec(x) = \frac{1}{ \cos(x) }$

$5) \tan(x) = \frac{ \sin(x) }{ \cos(x) }$

Solution :

we have to find the value of secx(1-sinx)(secx+tanx)

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$\sec x(1 - \sin x)( \sec x + \tan x)$

$= \frac{1}{ \cos x } (1 - sinx)( \frac{1}{cosx} + \frac{sinx}{cosx} )$

$= \frac{1 - \sin \: x }{cosx} \times ( \frac{1 + \sin x }{cosx} )$

$= \dfrac{1 - \sin {}^{2} x }{ \cos {}^{2} x}$

we know that 1-sin²A = cos²A

$= \dfrac{ \cos {}^{2}x }{ \cos {}^{2}x }$

$= 1$

it is the required solution!

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More Trigonometric Formula's:

• sin2A = 2 sinA cosA
• cos2A = cos²A - sin²A
• tan2A = 2 tanA / (1 - tan²A)