Question

prove that sinQ/1+cosQ +1+cosQ/sinQ=2cosec Q​

Answer 1

Answer:

Step-by-step explanation:

sinQ/1+cosQ +1+cosQ/sinQ=2 cosec Q

First multiply the denominators,

= sinQ(sinQ)/1+cosQ(sinQ) + 1+cosQ(1+cosQ)/sinQ(1+cosQ)

= sin2Q/sinQ+cosQsinQ + 1+cos2Q+2cosQ/sinQ+sinQcosQ

=sin2Q+1+cos2Q+2cosQ/sinQ+cosQsinQ

=2+2cosQ/sinQ+sinQcosQ

Now take 2 from the numerator and sinQ from the denominator,

2(1+cosQ)/sinQ(1+cosQ)

cancelling 1+cosQ from numerator and denominator,

=2/sinQ

=2cosecQ .   Proved!