Question

(SinA-cosA) (1+tanA+cotA) =secA/cosec sqr A - cosecA/sec sqr A, proofit

Answer 1

(sin a - cos a)(1 + tan a + cot a)

Multiply sin and cos separately with the other expression.

sin a (1 + tan a + cot a) - cos a (1 + tan a + cot a)

sin a + (sin a * sin a / cos a ) + (sin a * cos a / sin a) - cos a - (cos a * sin a / cos a) - (cos a * cos a /sin a )

as tan a = sin a / cos a and cot a = cos a / sin a

So,

sin a + sin^2 a / cos a + cos a - cos a - sin a - cos^2 a / sin a

sin^2 a / cos a - cos^2 a / sin a

Now,

sin^2 a = 1 / cosec^2 a and cos a = 1 / sec a

So,

we get,

sec a / cosec^ 2 a - cosec a / sec^2 a = RHS

Hence Proved