Question

(cos A/1-sin A ) + (cos A/1+sin A) = 2 sec A

Answer 1

Answer:

LHS=

1−sinA

cosA

+

1+sinA

cosA

=

(1−sin

2

A)

cosA(1+sinA+1−sinA)

=

cos

2

A

2cosA

=

cosA

2

=2secA=RHS

Hence proved.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

AnswEr :

$\star$ ${\bold\purple{\dfrac{Cos \ A}{1 + Sin \ A} + \dfrac{1 + Sin \ A}{Cos \ A} = 2 \ sec \ A}}$

• T A K I N G ⠀ L H S :

$\implies\sf \dfrac{Cos \ A}{ 1 + Sin \ A} + \dfrac{1 + Sin \ A}{Cos \ A} \\\\\\:\implies\sf\dfrac{ Cos^2 A + \Bigg[1 + Sin \ A \Bigg]^2}{\Bigg[1 + Sin \ A \Bigg] Cos \ A} \\\\\\:\implies\sf \dfrac{ Cos^2 \ A + 1 \ Sin^2 \ A + 2 \ Sin \ A}{\Big[1 + Sin \ A \Big] + Cos \ A}\\\\\\:\implies\sf \dfrac{ 2 + 2 \ Sin \ A}{Cos \ A \Big[ 1 + Sin \ A \Big]}\\\\\\:\implies\sf \dfrac{ 2}{Cos \ A} \\\\\\:\implies{\bold\purple{ 2 \ Sec \ A}}$

$\qquad\qquad{\bold\pink{Hence \ Proved!!}}$