Question

Prove the following trigonometric identities:
1/secA+tanA-1/cosA-1/cosA=1/cosA-1/secA-tanA

Answer 1

The correct question is,

Prove the following trigonometric identities:

1/secA+tanA-1/cosA=1/cosA-1/secA-tanA

Hence it is proved that 1/secA+tanA-1/cosA=1/cosA-1/secA-tanA

Given,

1/secA+tanA-1/cosA-1/cosA=1/cosA-1/secA-tanA

Consider,

1/secA+tanA

rationalizing the above factor, we get,

1/secA+tanA = secA-tanA

Now, we have,

LHS

1/secA+tanA-1/cosA

= secA-tanA-1/cosA

= secA-tanA-secA

= secA -(tanA+secA)

= secA -(tanA+secA) × [(tanA-secA) / (tanA-secA)]

= secA -(tan^2A-sec^2A) / (tanA-secA)

= 1/cosA - 1/secA-tanA

RHS

Hence proved.