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If x= cosecA + cosA and …

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If x= cosecA + cosA and y= cosecA- cosA then prove that (2÷x+y)^2 + (x-y÷2)^2 -1 =0

Posted by Ayush Singh 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

x = cosec A + cos A and y = cosec A - cos A
Thus, we have
x + y = cosec A + cos A + cosec A - cos A = 2 cosec A
x - y = cosec A + cos A - cosec A + cos A = 2 cos A
L.H.S = {tex}\left( \frac { 2 } { x + y } \right) ^ { 2 } + \left( \frac { x - y } { 2 } \right) ^ { 2 } - 1{/tex}
{tex}= \left( \frac { 2 } { 2 \cos e c A } \right) ^ { 2 } + \left( \frac { 2 \cos A } { 2 } \right) ^ { 2 } - 1{/tex}
{tex}= \left( \frac { 1 } { \text{cosec} A } \right) ^ { 2 } + ( \cos A ) ^ { 2 } - 1{/tex}
= (sin A)² + (cos A)² - 1
= sin²A + cos²A - 1
= 1 - 1
= 0
= R.H.S

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CBSE > Class 10 > Mathematics