Any tips of solving Simplify, verify and prove?

I feel so bad when solving these types of question.(sin cos tan sec csc cot)

Hi XavierZz     

Lets see

Reciprocal ratios

cot=1/tan         see how the 3rd letter in the less familiar one = the first letter in the 'normal' one

sec=1/cos        see the 3rd/1st leter thing again

cosec=1/sin     and  again  (in Australia we write cosec not just csc

Complementary ratios

Remember: Complementary angels add up to 90 degrees

\(cosine\theta=sine(90-\theta) \;and\; vise\; versa \\ cotangent\theta=tangent(90-\theta) \;and\; vise\; versa \\ cosec \theta=sec(90-\theta) \;and\; vise\; versa \\\)

The 'co' stands for complimentary.

Identities that you need to remember are

\(\\~\\ \boxed{cos^2\theta+sin^2\theta=1\\~\\ sin(x+y)=sinxcosy+cosxsiny\\~\\ cos(x+y)=cosxcosy-sinxsiny\\}\)

Just about everything else can be worked out from there.

I don't think I remember anything much else but most people remember a few more because it takes them too long or it is too difficult for them to derive other things.

NOW IT IS JUST A MATTER OF PRACTICE, PRACTICE AND MORE PRACTICE.