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Ask QuestionPosted by Santosh Patel 7 years, 7 months ago
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Posted by Jaspreet Singh 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
(1 + cot A + tan A)(sin A - cos A)
= sin A - cos A + cot A sin A - cot A cos A + tan A sin A - tan A cos A
=sin A - cos A + {tex}\frac{cos A}{sin A}{/tex} {tex}\times{/tex} sin A - cot A cos A + tan A sin A - {tex}\frac{sin A}{cos A}{/tex} {tex}\times{/tex} cos A
=sin A - cos A + cos A - cot A cos A + tan A sin A - sin A
=sin A tan A - cot A cos A
Posted by Fahad Naseem 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
If a and b are odd numbers then it should be in 2q+1 or 2q+3 form where q is a positive integer.
Let a = 2q + 3 , b = 2q + 1 and a > b
Now, {tex}\frac{a + b } {2} = \frac{ 2q + 3 + 2q + 1}{2}{/tex}
{tex}= \frac { 4 q + 4 } { 2 }{/tex}
= 2q + 2
{tex}\frac{a+b}{2}{/tex}=2(q+1) = an even number..........(1)
Now
{tex}\frac { a - b } { 2 } = \frac { ( 2 q + 3 ) - ( 2 q + 1 ) } { 2 }{/tex}
{tex}= \frac { 2 q + 3 - 2 q - 1 } { 2 }{/tex}
{tex}\frac{a-b}{2}= \frac { 2 } { 2 }{/tex} = 1 = an odd number..........(2)
Hence From (1) and (2) {tex}\frac{a+b}{2}{/tex} and {tex}\frac{a-b}{2}{/tex} are even and odd numbers respectively
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