Question

Proving Identities :

1)tan X = sin X Sec X

2)sec X = sin X tan X + Cos X

3) tan X sin X = sec X - cos X

4) sec X - tan X = 1 - sin X / cos X

5)tan X sin X = sec X - Cos X

Answer 1

Hey dear here is your answer!!!!!

We know tanX= sinX/cosX

1) tanX = sinX sec X

On solving LHS

Solution = SinX / Cos X
Sin X * 1/Cos X
Sin X * SecX
Hence prooved LHS = RHS

2) sec X = sin X tan X + Cos X
=Sin X * Sin X / Cos X + Cos X
=Sin ^2 X + Cos ^2 X / Cos X
= 1/cos X
= sec X
Hence prooved LHS= RHS

3) Tan X sin X = sec X - cos X
sin X / cos X * sin X
sin ^2 X /cos X
1-cos^2 X / cos X
sec X - cos X
Hence prooved LHS= RHS

4) sec X- tan X = 1-sin X / cos X
1/cos X - sin X/cos X
1-sin X / cos X
Hence prooved LHS= RHS

5)tan X Sin X = sec X- Cos X
sin X/cos X* sin X
sin^2 X / cos X
1-cos^2 X / cos X
sec X - cos X
Hence prooved LHS= RHS
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Hope it helps u dear....