Question

Prove that: cos/1+ sin+ 1+sin/cos=2sec

Answer 1

Q - cos/(1+sin) + (1+sin)/cos

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= cos^2 + (1+sin)^2 / cos (1+sin)

= cos^2 + 1 + 2sin + sin2 / cos (1+sin)

We know that cos^2 + sin^2 = 1

= (1+1+ 2sin) / cos(1+sin)

= (2 + 2sin) /cos (1+sin)

= 2(1+sin) / cos (1+sin)

= 2 / cos

= 2sec Proved

Answer 2

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \orange{ to \: prove :}} \\ { \pink{ \boxed{ \red{ \frac{ \cos(a) }{1 + \sin(a) } + \frac{1 + \sin(a) }{ \cos(a) } = 2 \sec(a) }}}}$

☆ USING TRIGO IDENTITY TO PROOF:

$\to\frac{cos(a) }{1 + \sin(a) } + \frac{1 + \sin(a) }{ \cos(a) } = 2 \sec(a) \\ \: \: \: \: \: \: \: LHS \\ \to \frac{cos(a) }{1 + \sin(a) } + \frac{1 + \sin(a) }{ \cos(a) } \\ \to \frac{ \cos ^{2}(a ) + (1 + { \sin(a) })^{2}}{(1 + \sin(a)) \cos(a) } \\ \to \frac{ \cos ^{2} (a) + 1 + { \sin^{2} (a) } + 2 \sin(a) }{(1 + \sin(a) ) \cos(a) } \\ \to \frac{1 + 1 + 2 \sin(a) }{(1 + \sin(a)) \cos(a) } \\ \to \frac{2 + 2 \sin(a) }{(1 + \sin(a)) \cos(a) } \\ \to \frac{2(1 + \sin(a)) }{(1 + \sin(a) ) \cos(a) } \\ \to \frac{2}{ \cos(a) } \\ \to \frac{2}{ \frac{1}{ \sec(a) } } \\ \to 2 \sec(a) \\ LHS=RHS$

$\huge{\pink{\boxed{\green{\underline{\sf{VERIFIED}}}}}}$

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