PT; sinФ(1+tanФ)+cosФ(1+cotФ)=secФ+cosecФ
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LHS=sin a (1+tan a) + cos a(1+cot a)
=sin a(1+sina÷cos a)+ cos a(1+cos a÷sin a)
=sin a((cos a + sin a)÷cos a)÷cos a((cos a+sin a)÷sin a)
=(sin^a(cos a +sin a)+cos^(cos a+sin a))÷sin a×cos a
=(sin^a +cos^a(cos a+sin a))÷sin a×cos a
(sin^ a+cos^ a= 1)
=( cos a + sin a)sin a×cos a
=1÷cos a+1÷sin a
=sec a + cosec a
LHS = RHS
=sin a(1+sina÷cos a)+ cos a(1+cos a÷sin a)
=sin a((cos a + sin a)÷cos a)÷cos a((cos a+sin a)÷sin a)
=(sin^a(cos a +sin a)+cos^(cos a+sin a))÷sin a×cos a
=(sin^a +cos^a(cos a+sin a))÷sin a×cos a
(sin^ a+cos^ a= 1)
=( cos a + sin a)sin a×cos a
=1÷cos a+1÷sin a
=sec a + cosec a
LHS = RHS
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