Question

If a and b are complementary angles, prove that
cos b+ cot b= sec a cos b(1+sin b)

Answer 1

if a and b are complementary angles
a+b =90
a=90-b---(1)
rhs =sec a cos b(1+ sinb)

=sec(90-b)cosb(1+sinb)since from(1)
=cosecbcosb(1+sinb)
=1/sinb*cosb(1+sinb) since cosecb=1/sinb
=cotb(1+sinb)
=cotb+cotbsinb
=cotb+cosb
=cosb+cotb
=lhs

Answer 2

Step-by-step explanation:

Here is the answer........