Question

how to solve any trigonometric identities easily,any tips plzzz??

Answer 1

Do practice regularly of trigonometry and you can also use some reference books for understanding

Answer 2

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.