Prove that cosA/1+sinA + 1+sinA/cosA =2secA
explain deeply
Answers
Answered by
4
The answer is in the page full prove
Attachments:
syedairam:
thank you
Answered by
1
cosA/1+sinA + 1+sinA/cosA
Firstly rationalise it,
cosA / ( 1+ sinA)× (1 - sin A)/ (1-sin A) + 1+sinA/cosA
cosA ( 1- sinA)/ (1^2 - sin^2A) + (1 + Sin A) / cos A
{ by applying identity sin^2A+ cos^2A= 1 }
cosA ( 1- sinA) / cos^2 A + (1 + Sin A) / cos A
{ cosA ( 1- sin A) + cos A ( 1 + sinA) } / cos^2 A
Take cos A common
cosA ( 1 - sin A + 1 + sin A) / cos^2A
2 cos A / cos^2A
2 / cos A
= 2× 1 / cosA
= 2 secA ( because 1 ÷ cos A = Sec A )
Hope this helps you dear.
Firstly rationalise it,
cosA / ( 1+ sinA)× (1 - sin A)/ (1-sin A) + 1+sinA/cosA
cosA ( 1- sinA)/ (1^2 - sin^2A) + (1 + Sin A) / cos A
{ by applying identity sin^2A+ cos^2A= 1 }
cosA ( 1- sinA) / cos^2 A + (1 + Sin A) / cos A
{ cosA ( 1- sin A) + cos A ( 1 + sinA) } / cos^2 A
Take cos A common
cosA ( 1 - sin A + 1 + sin A) / cos^2A
2 cos A / cos^2A
2 / cos A
= 2× 1 / cosA
= 2 secA ( because 1 ÷ cos A = Sec A )
Hope this helps you dear.
Similar questions