Prove the following trig identities

Question

3, 9 and 7. Use the above numbers to prove only three of these trig identities.

sin x/ 1 + cos x = 1 - cos x/sin x

1/ 1 + Cos x = csc^2 x - cot x/sinx x

-sin x - cos x cot x= - csc x

1 + tan x/ 1 + cot x = tan x

Answer 1

#1)

sin^2 + cos^2 = 1

sin^2 = 1 - cos^2

sin^2 = (1+cos)(1-cos)

sin/(1+cos) = (1-cos)/sin

#2) csc^2 - cot/sin =

csc^2 - cos/sin^2

=1/sin^2 - cos/sin^2

=(1 - cos)/sin^2

=(1-cos)/(1-cos^2)

= (1-cos)/ [(1+cos)(1-cos)]

1/(1+cos)

#3)

-sin - cos*cos/sin =

(-sin^2-cos^2)/sin =

-(sin^2+cos^2)/sin =

-1/sin =

-csc

#4) multiplies everything by tangent...

(tan + tan^2)/ (tan + 1) =

tan( 1+ tan)/(tan+1) =

tan