Question

Prove that tanA/secA = sinA
${tan(a)\div \sec(a)}$
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Answer 1

Answer:

Step-by-step explanation:

Let’s see. We can start by writing it out, and then manipulating each side to make them equal.

sinA∗tanA+cosA=secA  

I usually convert things to sin and cos just to make it more familiar.

sinA∗sinAcosA+cosA=1cosA  

Now you can reduce the fraction on the left.

sin2AcosA+cosA=1cosA  

Now you can manipulate  cosA  to get a common denominator

sin2AcosA+cos2AcosA=1cosA  

Now that you have a common denominator, you can combine the fractions.

sin2A+cos2AcosA=1cosA  

And now since you (should) know that  sin2A+cos2A=1 , you can substitute that expression for 1, leaving you with:

1cosA=1cosA  

And voila!

Though you should think about why you couldn’t figure this out.

Before asking about it, you should have at least tried some manipulations to see if you can get anywhere. That is the way you will learn the best. Try to solve problems yourself and struggle to see the solution.

Only if you have been going in circles constantly should you just ask for the solution. Doing this will cause you to be more creative and a better problem solver.

Or perhaps you were unaware of how equations like that can be proven. In that case, you have your answer: write out the equation and manipulate each side individually until you arrive at a true statement.

Hope this helps!

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