Hi Guys,
Any #MathsAryabhatta
Can help me with some tips of solving trig proofs faster
and traingles proof faster and correctly.
Answers
hey,
Essential IdentitiesThe trick to solve trignogeometry
IT MIGHT TAKE SOME TIME TO READ THIS BUT IT IS WORTH IT!
How to Solve Them Correctly Every TimeThe following seven step process will work every time. It is rather tedious, and can take more time than necessary. As you gain more practice, you can skip or combine these steps when you recognize other identities.
STEP 1: Convert all sec, csc, cot, and tan to sin and cos. Most of this can be done using the quotient and reciprocal identities.
STEP 2: Check all the angles for sums and differences and use the appropriate identities to remove them.
STEP 3: Check for angle multiples and remove them using the appropriate formulas.
STEP 4: Expand any equations you can, combine like terms, and simplify the equations.
STEP 5: Replace cos powers greater than 2 with sin powers using the Pythagorean identities.
STEP 6: Factor numerators and denominators, then cancel any common factors.
STEP 7: Now, both sides should be exactly equal, or obviously equal, and you have proven your identity.
Example Problem Using the 7 Step Method
Show that cos4(x) - sin4(x) = cos(2x)
STEP 1: Everything is already in sin and cos, so this part is done.cos4(x) - sin4(x) = cos (2x)
STEP 2: Since there are no sums or difference inside the angles, this part is done.cos4(x) - sin4(x) = cos (2x)
STEP 3: cos(2x) is a double angle. Use the double angle formula: cos (2x) = cos2(x) - sin2(x), to simplify.cos4(x) - sin4(x) = cos2(x) - sin2(x)
STEP 4: Here is where your algebra knowledge comes in. In this case, we can see that the left side is a “difference of two squares"
[if you forgot: a2-b2 = (a+b)(a-b)]
Left side: cos4x - sin4x - (cos2(x))2 - (cos2(x))2 = (cos2(x)-sin2(x))(cos2(x)+sin2(x))
Now, our problem looks like this:(cos2(x)-sin2x))(cos2(x)+sin2(x))= cos2(x) - sin2(x)
The sides are almost the same
STEP 5: There are no powers greater than 2, so we can skip this step
STEP 6: Since cos2(x) - sin2(x) appears on both sides of the equation, we can cancel it.We are left with: cos2(x) + sin2(x) = 1
STEP 7: Since this is one of the pythagorean identities, we know it is true, and the problem is done.
some extra tips-
Extra TipsGet both sides of the equation in the same functions. You don’t always have to use sin and cos, but its easier to compare when both sides are composed of similar functions
Make sure all your angles are the same.
Learn the formulas by heart as they will help a lot ahead.
Once you are clear with the formulas move ahead with solving problems.
Always remember that the number of questions is irrelevant. Eg: there is no point in doing an exercise which repeats the same kind of questions again and again. Just do 3–4 of them and leave out the rest as they can be lot of timw wasting. Always remember Quality of the questions matters more than the quantity. It doesn't matter even if you do only 10 questions a day, just make those 10 questions worth it.
Lastly, I would say thay the only way of learning Maths and to be able to do it properly is be doing alone. The more you practice the more perfection you will gain. There's no shortcut to it. You have to be clear through the basics and as you progress your speed in problem solving will gradually increase..
Hope this helps :)
I m not aryabhatta but still...
GUD LUK
See what is asking in the question and accordingly go ahead with the solution
Practice as much as you can as we all know PRACTICE MAKES THE MAN PERFECT
Learn all the theorems
Hope it helps....