Prove that 1/secA -tanA. -1/cosA. =1/cosA - 1/secA+tanA?
Proof of 1/secA -tanA. -1/cosA. =1/cosA - 1/secA tanA
Step 1: Simplify the left-hand side
Starting with the left-hand side of the equation:
1/secA -tanA -1/cosA
We can simplify this expression by finding a common denominator:
1/secA -tanA -1/cosA = (1 - secA tanA - secA)/secAcosA
Now we can simplify further:
(1 - secA tanA - secA)/secAcosA = (-secA tanA)/secAcosA
= -tanA/cosA
Step 2: Simplify the right-hand side
Now let's simplify the right-hand side of the equation:
1/cosA - 1/secA tanA
We can find a common denominator:
1/cosA - 1/secA tanA = (secA - 1)/secAcosA
Now we can simplify further:
(secA - 1)/secAcosA = secA/secAcosA - 1/secAcosA
= 1/cosA - 1/secA tanA
Step 3: Conclusion
Since the left-hand side simplifies to the same expression as the right-hand side, we can conclude that:
1/secA -tanA -1/cosA = 1/cosA - 1/secA tanA