Question

sinA (1+tanA)+cosA(1+coto)
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Answer 1

Answer:secA+cosecA

I hope u will get the answer right

Answer 2

Question:

sinA(1 + tanA) + cosA(1 + cotA)

Used formulas:

sin²A + cos²A = 1

tanA = sinA/cosA

cotA = cosA/sinA

1/cosA = secA

1/sinA = cosecA

Answer:

$\sin(a) (1 + \frac{ \sin(a) }{ \cos(a) } ) + \cos(a) (1 + \frac{ \cos(a) }{ \sin(a) } )$

$\frac{ \sin(a)( \cos(a) + \sin(a)) }{ \cos(a) } + \frac{ \cos(a) ( \sin(a) + \cos(a)) }{ \sin(a) }$

$\frac{ { \sin }^{2}(a)( \sin(a) + \cos(a) ) + { \cos}^{2} (a)( \sin(a) + \cos(a) }{ \sin(a) \cos(a) }$

taking common sin(a) + cos(a)

$= \frac{ (\sin(a) + \cos(a) )( { \sin}^{2} (a) + { \cos}^{2}(a)) }{ \sin(a) + \cos(a) }$

$= \frac{ \sin(a) + \cos(a) }{ \sin(a) \cos(a) }$

$= \frac{ \sin(a) }{ \sin(a) \cos(a) } + \frac{ \cos(a) }{ \sin(a) \cos(a) }$

$= \frac{1}{ \cos(a) } + \frac{1}{ \sin(a) }$

$= \sec(a) + \cosec(a)$

Concepts used:

⟩⟩ trigonometric identities

⟩⟩ trigonometric ratios

Note:

If you have any doubts in using formula see in (used formulas