# Prove that sin^2 A/ cos ^2 A+ cos^2 A/sin^2 A= sec^2 *cosec^2 A -2

2
by g2000

2015-08-07T19:55:00+05:30

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Sin^2A/cos^2A  +  cos^2A/sin^2A
on taking lcm
sin^4A + cos^4A
sin²A cos²A
(sin²A + cos²A)² - 2sin²Acos²A              (sin²A+cos²A=1)
sin²Acos²A
⇒  1 - 2sin²Acos²A                              (1/sinA = cosecA  ,1/cosA=secA)
sin²Acos²A
cosec²Asec²A - 2  = RHS
Hence proved
2015-08-07T19:59:28+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Sin^2A/cos^2A  +  cos^2A/sin^2A
on taking lcm
sin^4A + cos^4A
sin²A cos²A
⇒ (sin²A + cos²A)² - 2sin²Acos²A
sin²Acos²A
⇒  1 - 2sin²Acos²A
sin²Acos²A
cosec²Asec²A - 2  = RHS
Hence proved
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