Question

prove (1+cot alpha -sec (alpha+pi÷2) (1+cot alpha + sec (alpha +pi÷2))

Answer 1

{ 1 + cotx - sec( x  + π/2) } { 1 + cotx + sec( x + π/2) }
 
 = {1 + cotx - (- cosecx) } { 1 + cotx + (- cosecx) }

= { 1 + cotx + cosecx} { 1+ cotx - cosecx}

= { ( 1 + cotx) ² - cosec²x}

= 1 + cot²x + 2cotx - cosec²x

= 1 - (cosec²x - cot²x ) + 2cotx

= 1 - 1 + 2cotx             [ cosec²x - cot²x = 1 ]

=2cotx

Hence proved.

Answer 2

Here is the answer

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