How to solve these limits ?

What is $\frac{1}{\sqrt{2}}$? Can you write it in a trigonometric form?
And expand cot(x) as cos(x)/sin(x).
$\frac{1}{\sqrt{2}}$ as cos π/4 or sin π/4 ?

OMG..sorry...it's not x to a ,but x to 0....sorry
Do you know the definition of derivative of a function in limit form? Question (2) is the simple definition of derivative of f(y) in that form. All you need to do is find what f(y) is and then find f'(y).

Do you know the definition of derivative of a function in limit form? Question (2) is the simple definition of derivative of f(y) in that form. All you need to do is find what f(y) is and then find f'(y).
urgh..then its the derivative of ysec(y)....so then ?
Is it the answer ?-ysec(y) ?

urgh..then its the derivative of ysec(y)....so then ?
Is it the answer ?-ysec(y) ?
Yes, the answer is the derivative of y*sec(y). But you need to apply product rule while differentiating this function!!

Yes, the answer is the derivative of y*sec(y). But you need to apply product rule while differentiating this function!!
We have not such rule in Limits but in differential calculus we were taught,
y=f(x)g(x)
$\frac{dy}{dx}$=g(x)f'(x)+f(x)g'(x)

We have not such rule in Limits but in differential calculus we were taught,
y=f(x)g(x)
$\frac{dy}{dx}$=g(x)f'(x)+f(x)g'(x)
Exactly. Use this rule to differentiate y*sec(y), that's the answer you are looking for!

Convert $\frac{1}{\sqrt{2}}$ into $cos(\frac{\pi}{4})$, and apply the formula that changes the difference of two trigonometric terms into their product. In the denominator, after writing cot in terms of cos and sin, try getting a single trigonometric ratio and simplify.