How can you prove #(Seca+coseca)/(tana+cota)=sina+cosa#?

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Answer 1 · 2018-05-17T05:17:42

#color(blue)(=> sin a + cos a#

#(sec a + csc a) / (tan a + cot a)#

#=> (1/cos a + 1/sin a) / (sin a / cos a + cos a / sin a)#

#=> (sin a + cos a) / cancel(sin a cos a) / (sin^2 a + cos ^2 a) / cancel(sin a cos a)#

#=> (sin a + cos a) / (sin^2 a + cos^2 a)#

But #sin^2 a + cos ^2 a = 1#, identity

#color(blue)(=> sin a + cos a#

#LHS = RHS#