# Help me prove these trigonometric identities??? PLEASE HELP! :(?

Can someone help me prove the following identities??? Please explain how you did so as well. I have a quiz tomorrow and could use the help :-)

1. sinx cosx tanx - 1 = -cos2x

2. sin2x ( cos2x/sin2x + 1 ) = 1

3. Tan2x = sin2x ( 1 + tan2x )

Help is reallllyyy appreciated! Please help guys! :-(

### 1 Answer

Relevance

- 1 decade agoFavorite Answer
1. LHS = sinx cosx tanx - 1

= sinx cosx (sinx/cosx) - 1

= sin²x - 1

= -(1 - sin²x)

= - cos 2x = RHS

Hence proved

2. LHS = sin²x(cos²x/sin²x + 1)

= sin²x[(cos²x + sin²x)/sin²x]

= cos²x + sin²x

= 1 = RHS

Hence proved

3. RHS = sin²x (1 + tan²x)

= sin²x + sin²xtan²x

= sin²x + (sin^4x/cos²x)

= (sin²xcos²x + sin^4x)/(cos²x)

= sin²x(cos²x + sin²x)/cos²x

= sin²x/cos²x

= tan²x = LHS

Hence proved

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