Question

secA +tanA/secA-tanA - secA -tanA /secA +tanA​

Answer 1

Answer:

0

Step-by-step explanation:

secA + tanA/secA - tanA - secA - tanA/secA + tanA

= secA - secA + tanA/secA - tanA/secA - tanA + tanA

= 0

Answer 2

Question :

Solve $\dfrac{ \sec(a) + \tan(a) }{ \sec(a) - \tan(a) } - \dfrac{ \sec(a) - \tan(a) }{ \sec(a) + \tan(a) }$

Trigonometric Formula's:

1. sin²A + cos²A = 1
2. sec²A - tan²A = 1
3. cosec²A - cot²A = 1

Solution :

$\dfrac{ \sec(a) + \tan(a) }{ \sec(a) - \tan(a) } - \dfrac{ \sec(a) + \tan(a) }{ \sec(a) + \tan(a) }$

⇒Take LCM

$= \frac{( \sec(a) + \tan(a)) {}^{2} - ( \sec(a) - \tan(a)) {}^{2} }{( \sec(a) - \tan(a))( \sec(a) + \tan(a) ) }$

$= \frac{( \sec {}^{2} (a) + \tan {}^{2} (a) +2 \tan(a) \sec(a)) - ( \sec {}^{2} (a) + \tan {}^{2} (a) - 2 \tan(a) \sec(a) ) }{ \sec {}^{2} (a) - \tan {}^{2} (a) }$

we know that sec²A - tan²A = 1

$= 4 \sec(a) \tan(a)$

it is the required solution!

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More Trigonometric Formula's:

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