How Do You Prove These Trigonometric Identities?

[Cutie123]

Can someone please help me with these two questions.

Th first one is prove:

1-tan^2x
________ = cos2x
1+tan^2x

& the second one is

prove:

sinx+ sinxcot^2 = secx

 

[rebedotcca]

Can someone please help me with these two questions.

Th first one is prove:

1-tan^2x
________ = cos2x
1+tan^2x

& the second one is

prove:

sinx+ sinxcot^2 = secx

1)

1-tan^2x
________ = cos2x
1+tan^2xLHS : [1 - (sin^2x/ cos^2x) ] / [ 1 + (sin^2x/cos^2x)]

= [(cos^2x -sin^2x)/cos^2x] X [cos^2x/(cos^2x + sin^2x)]

= (cos^2x - sin^2x) / (cos^2x +sin^2x ) (Rmb cos^2x + sin^2x =1 )

= cos^2x -sin^2x

= cos^2x - (1 - cos^2x)
= 2cos^2x -1 (double angle formula)
= cos2x = RHS
for question 2, did you miss out an x beside cot^ ?