for Q1,
from LHS
sin x / cos x + cos x / sin x
= [ (sin x)^2 + (cos x)^2 ] / [sin x cos x]
= 1 / sin x cos x
= 2 / 2sin x cos x
= 2 / sin 2x
= 2 cosec 2x
for some tips and strategies for proving trigo identities check
out
http://a-maths-tuition.blogspot.com/2010/02/proving-trigo-identities-part-i.html
for q2
2 cosec 2x = 3 tan x + 1
tanx + cotx = 3 tan x + 1
multiply by tan x throughout
(tanx)^2 + 1 = 3 tanx + 1
you will end up with a quadratic equation
then can solve for tan x
for more info on how to solve trig equations check out
http://www.a-maths-tuition.com/2010/02/trigo-equations-part-iii.html