HCU MCA 2013 Paper

Question : 75 of 75

Marks: +1, -0

The value of the expression

1 - { \cos ^ { 2 } x }/ { 1 + \sin x } + { 1 + \sin x }/ { \cos x } - { \cos x } /{ 1 - \sin x }

is equal to

Solution:

E = 1 - { \cos ^ { 2 } x } /{ 1 + \sin x } + { 1 + \sin x }/ { \cos x } - { \cos x } /{ 1 - \sin x }

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

= 1 + { ( 1 + \sin x ) }/ { \cos x } - { \cos x } /{ ( 1 - \sin ^ { 2 } x ) } [ \cos x ( 1 - \sin x ) + ( 1 + \sin x )]

= 1 + { ( 1 + \sin x ) } /{ \cos x } - { \cos x }/ { \cos ^ { 2 } x } \{ \cos x - \sin x . \cos x + 1 + \sin x \}

= 1 + { 1 }/ { \cos x } \{ 1 + \sin x - \cos x + \sin x.\cos x - 1 - \sin x \}

= 1 + { 1 } /{ \cos x } \{ \sin x . \cos x - \cos x \}

= 1 + \sin x - 1

= \sin x

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